Question

Note: this is not a question but a tutorial on basic steps inolved in proving identities. I will upload an advanced one later

some technical problem and i am not able to upload the attachment.

Answer 1

Uploading an attachment.

Answer 2

Rules to Prove identities.

1) Convert every ratio into Sinθ and Cosθ

2) Take Lowest Common Multiple If fractions are still visible

3) Use sin^2 + Cos^2 =1 When needed

4) Use a^2 - b^2 = (a-b)(a+b)

5)Rationalize if none of the above work
e.g

1/5+x

it can be rationalized my multiplying and dividing it with its conjugate pair

1/5+x * 5-x/5-x

this will give 5-x/5^2 - x^2

6) then there is a special rule which involves directly using identities of
Cos^2 , Tan^2 and Sin^2

Answer 3

by*

Answer 4

tan^2(x) + 1 = sec^2(x)

cot^2(x) + 1 = csc^2(x)

Answer 5

just a correction on terms..

\(\large \frac{1}{5 -x} \times \frac{5+x}{5+x}\) is not rationalization. this is multiplying by the conjugate. rationalization involves a square root.

But anyway...good work! ^_^

Answer 6

my bad and thanks for the correction

Answer 7

keep on sharing :)

Answer 8

Note - use the following to reduce other trig functions to sin and cos
sec=1/cos
csc=1/sin
tan=sin/cos
cot=cos/sin