Question

PROVING IDENTITIES!!

Answer 1

qn?

Answer 2

the answer is a calculator

Answer 3

\[(\sin x + \cos x)(\tan x + \cot x) =\sec x + \csc x\]

Answer 4

Change to sin and cos then FOIL it out

Answer 5

Ok.

We have -

(sin x + cos x ) (sinx/cosx + cosx/sinx) (since tan x = sinx/cosx and cot x = cosx/sinx)

=> (sin x + cos x) (sin^2x + cos^2x/ sin x . cos x)

=> (sin x + cos x) ( 1/sin x. cos x ) (since sin^2x + cos^2x = 1)


=> (sin x + cos x)/sin x. cos.x


Separating sin x, cos x in numerator with common denominator,

sin x / sin x. cos x + cos x . / sin x cos x

=> 1/cos x + 1/sin x

=> sec x + csc x (since 1/cos x = sec x, 1/sin x = csc x)

Proved

Answer 6

\[(\sin x + \cos x)(\frac{ \sin x }{ \cos x }+\frac{ \cos x }{ \sin x })\]
\[(\sin x + \cos x)(\frac{ \sin ^2 x + \cos ^2 x}{ \cos x \sin x })\]
\[(\sin x + \cos x)(\frac{ 1 }{ \cos x \sin x })\]

Answer 7

i got it....thank you all...