The trigonometric identity?

Question

I need help now. Someone help me, please.
Use the trigonometric identity to find the value of angel

sin (2Q) + cos (2Q) = 0

Q= angel

Thanks you.

Answer 1

Don't be faked out by the 2Q thing.

Let x = 2Q

Then the equation turns into sin x + cos x = 0
or
sin x = -cos x

Contemplate your unit circle for a while, and you should see that this is true when x = 135 degrees or x = 315 degrees.

But x = 2Q
so Q = x/2

Hence, the answers are 67.5 degrees and 157.5 degrees.

If they want you to stick to the interval between 0 and 90 degrees, then the answer would of course be 67.5 degrees.

Answer 2

sin(2Q) + cos(2Q) = 0
√2{(1/√2) sin(2Q) + (1/√2) cos(2Q) }= 0
(1/√2) sin(2Q) + (1/√2) cos(2Q) = 0
cos(π/4) sin(2Q) + sin(π/4) cos(2Q) = 0
sin(π/4 + 2Q)=0
π/4 + 2Q=…, 0, π, 2π, 3π, …
2Q=…, 0-π/4, π-π/4, 2π-π/4, 3π-π/4, …
2Q=…, -π/4, 3π/4, 7π/4, 11π/4, …
Q=…, -π/8, 3π/8, 7π/8, 11π/8, …

or

Q=…, -180/8(°), 3*180/8(°), 7*180/8(°), 11*180/8(°), …
Q=…, -22.5(°), 67.5(°), 157.5(°), 247.5(°), …