Question

solve sin^2x-cos^2x=1\2 please help

Answer 1

Answer: sinx = √3/2    and     cosx = 1/2

Step-by-step explanation:

we know that sin^2x + cos^2x = 1     ......(1)

and given that sin^2x-cos^2x=1\2    .......(2)

adding both: 2sin^2x = 1 +1/2⇒ 2sin^2x = 3/2⇒sin^2x=3/4⇒sinx = √3/2

putting sin^2x = 3/4 in equation 1:

3/4 +cos^2x = 1

cos^2x = 1-3/4

cos^2x = 1/4

cosx = 1/2

Answer 2

We know that,

sin²x + cos²x = 1

From the above, we can derive sin²x = 1 - cos²x

Substitute sin²x value in the equation given in question.

sin²x - cos²x = 1/2

1 - cos²x - cos²x = 1/2

1 - 2cos²x = 1/2

-2cos²x = -1/2

cos²x = 1/4

cosx = 1/2

cos60° = 1/2

x = 60°

Hope this helps you