Question

If tan²x = 2 tan²y +1, show that cos 2x + sin²y = 0.
.. the ques is taken from APC
ml-aggarwal- cls11 isc bk​

Answer 1

Answer:

Proved :  cos 2x + sin²y = 0

Step-by-step explanation:

The given equation is:

⇒  tan²x  =  2 tan²y  + 1

Adding 1 both side, we get:

⇒  tan²x  +  1 =  2 tan²y  + 1  + 1

⇒  tan²x  +  1 =  2 tan²y  +  2

⇒  sec²x  =  2 ( tan²y  +  1 )

⇒  sec²x  =  2 sec²y

⇒  cos²x  =  $\frac{1}{2}$ cos²y

⇒  2 cos²x  =  cos²y

Subtracting 1 from both sides, we get:

⇒  2 cos²x - 1 =  cos²y - 1

⇒ cos 2x  =  - ( 1 - cos²y )

⇒ cos 2x  = - sin²y

∴  cos 2x  + sin²y  =  0

Hence, proved