Question

Show that Cos²theta- Sin² theta = 2Tantheta/ 1 - tan² theta

Answer 1

Hii friend,

Let @ be a theta.

Putting @ = 30° , we find

LHS = (Cos²@ - Sin²@)


= [(✓3/2)² - (1/2)²] = (3/4-1/4) = 2/4 = 1/2

RHS = 2tan30°/ 1 - tan²30°


= 2×1/✓3/[1-(1/✓3]² = 2/✓3/ 1-1/3 = 2/✓3 × 3/2 = ✓3.

THEREFORE,

LHS IS NOT EQUAL TO RHS.

HENCE,

THE GIVEN EQUATION IS NOT AN IDENTITY.


HOPE IT WILL HELP YOU.... :-)

Answer 2

The answer is given below :

Now, L.H.S.

$= {cos}^{2} \alpha - {sin}^{2} \alpha \\ \\ = cos2 \alpha$

and R.H.S.

$= \frac{2tan \alpha }{1 - {tan}^{2} \alpha } \\ \\ = tan2 \alpha$

So, L.H.S. does not equal to R.H.S.

EXAMPLE :

We put $\alpha=0$

Then, L.H.S. = cos0 = 1

and

R.H.S. = tan0 = 0

So, L.H.S. and R.H.S. be not equal.

Thank you for your question.