Question

(2)
If
sin
$\sin(0)$
+ sin2 0 = 1,
show that :
cos2 0 + cos4 0 = 1.​

Answer 1

Answer:

Explanation:

Our starting goal is to turn all terms into cosine. Use the identity  

sin 2 θ + cos 2 θ = 1

sin a + 1 − cos 2 a = 1  sin a − cos 2 a = 0  sin a = cos 2 a

Square both sides to get rid of the sine.

( sin a ) 2 = ( cos 2 a )

2 sin 2 a = cos 4 a

Reuse

sin 2 θ + cos 2 θ = 1

:  1 − cos 2 a = cos 4 a 1 = cos 4 a + cos 2 a

Hopefully this helps!