Question

PT tan (θ+30) + cot(θ-30) = 1/sin2θ - sin60.

Answer 1

@waterineyes

Answer 2

Is that whole in denominator on right hand side ??

Answer 3

dividing sign ?

Answer 4

\[\tan(A +B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \tan(B)}\]

Answer 5

Your right hand side is this??

\[\frac{1}{\sin(2 \theta) - \sin(60)}\]

Answer 6

yes

Answer 7

\[\tan(\theta + 30) = \frac{\sqrt{3} \tan(\theta) + 1}{\sqrt{3} + \tan(\theta)}\]

Answer 8

Because:

\[\tan(30) = \frac{1}{\sqrt{3}}\]

Answer 9

okay

Answer 10

Sorry:

Negative sign will be there in denominator:

\[\tan(\theta + 30) = \frac{\sqrt{3} \tan(\theta) + 1}{\sqrt{3} - \tan(\theta)}\]

Answer 11

okay .. what about cot ?

Answer 12

cot formula ?

Answer 13

If you don't know the formula for cot then you can write that cot as 1/tan..

Answer 14

Do you know the formula for cot ??

Answer 15

yes

Answer 16

Okay then can you use that ??

Answer 17

cot (A+B) = cot A cot B - 1 / cot B+cot A

correct ?

Answer 18

Oh I think we are going in lengthy way..

Answer 19

?

Answer 20

See I think if we will do this way then it may get easy..

Answer 21

\[\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

Answer 22

For simplicity now : Let theta + 30 = x and theta - 30 = y:

\[\frac{\sin(x)}{\cos(x)} + \frac{\cos(y)}{\sin(y)} \implies \frac{\sin(x)\sin(y) + \cos(x) \cos(y)}{\cos(x) \sin(y)}\]

Answer 23

\[\sin(x) \sin(y) + \cos(x)\cos(y) \implies \cos(x - y)\]

Answer 24

y did yu delete ?

Answer 25

\[x - y \implies \theta + 30 - \theta + 30 = 60\]

Answer 26

I have used wrong formula for numerator..

now this one I have used is right.

So the numerator is now :

\[\cos(60) = \frac{1}{2}\]

Answer 27

So the whole thing has now become:

\[\implies \frac{1}{2\cos(x) \sin(y)}\]

Getting till here??

Answer 28

yes

Answer 29

Tell me the step you are not getting I will explain you then in far better way than this ??

Answer 30

no i understand

Answer 31

Are you sure you have got till here ??

Answer 32

oh yes water ;)

Answer 33

Can you solve the denominator now ??

Answer 34

will try

Answer 35

hold

Answer 36

Ok, held on..

Answer 37

am trying to do this sum frm d begining on my own by using the formula yu said , oly then will i first know if i have any doubt !

Answer 38

Meaning ??

Answer 39

You are going to solve it by using tan ????

Answer 40

am just gonna try re-doin what you did just to make sure everything got in

Answer 41

Okay..

But don't forget that you are going to solve for denominator part on your own..
For this part I mean:

\[2 \cos(x) \sin(y)\]

Answer 42

doubt !

Answer 43

Where ??

Answer 44

well this one , sinX sinY + cosX cosY = cos(X-Y)

Answer 45

how cos(X-Y) ?

Answer 46

I guessed the same..

ha ha ha..

Answer 47

Do you know the formula for cos(x-y) ???

Answer 48

\[\cos(x-y) = \cos(x) \cos(y) + \sin(x) \sin(y)\]

Answer 49

yes

Answer 50

See if x and y are greater than one another that will not change the formula because:

\[\cos( - \theta) = \cos(\theta)\]

Answer 51

yes

Answer 52

What is your numerator now tell me ??

Answer 53

what numerator ?

Answer 54

The part where you had doubt write that part..

Answer 55

sin(X) sin(Y) + cos(X) cos(Y) = cos(X-Y)

Answer 56

\[\frac{\sin(x)}{\cos(x)} + \frac{\cos(y)}{\sin(y)} \implies \frac{\sin(x)\sin(y) + \cos(x) \cos(y)}{\cos(x) \sin(y)}\]

Yeah here can you use that formula now ??

Answer 57

water yu havn't yet solved my doubt .. i asked yu how cos(X-Y)

Answer 58

@waterineyes ?

Answer 59

It is a basic identity...

Answer 60

i duno

Answer 61

\[\cos(x + y) = \cos(x)\cos(y) - \sin(x) \sin(y)\]
\[\cos(x-y) = \cos(x) \cos(y) + \sin(x) \sin(y)\]

Answer 62

i kno this

Answer 63

Can you remember these?

I thought you know this..

Answer 64

yea i kno

Answer 65

You know this and you don't know that how?

They are the same I think..

Answer 66

how WATER ?

Answer 67

Note that two identities in your notebook and remember those identities..

Answer 68

Are you asking for the proof of cos(x-y) ??

Answer 69

let me think .. what is happening

Answer 70

These are basic identities you have to remember..

If you are asking for proof then I can tell you in detail next saturday I have to go now.

For that last denominator part :

use this formula:

\[2\cos(x) \sin(y) = \sin(x + y) - \sin(x - y)\]
After using this you will get right hand side..

Answer 71

okay understood

Answer 72

thanks @waterineyes

Answer 73

Just try once you will get that we are close to right hand side...

Bye take care ashna..

Answer 74

Welcome..