Question

solve this trigonometry please​

Answer 1

Answer:

Step-by-step explanation:

Given: sin4θa+cos4θb=1a+b

To Prove: sin8θa3+cos8θb3=1(a+b)3

sin4θa+cos4θb=1a+b

b(1−cos2θ)2+acos4θ=aba+b

b−2bcos2θ+(a+b)cos4θ=aba+b

ab+b2−2b(a+b)cos2θ+(a+b)2cos4θ=ab

Let (a+b)cos2θ=x

x2−2bx+b2=0

Or (x−b)2=0

or x=b

or cos2θ=ba+b

Similarly,

sin2θ=aa+b

sin8θa3+cos8θb3

=a(a+b)4+b(a+b)4

=1(a+b)3