Question

Solve question 3 (see the attachment).

Answer 1

Answer:

sin^6theta + cos^6theta - 1 = lambda.sin²theta.cos²theta. here the lambda = -3

can be written as

sin^6theta + cos^6theta

sin^6theta + cos^6theta = 1 + lambda.sin²theta.cos²theta

cubing the identity ( sin²theta + cos²theta=1)

we get

( sin²theta + cos²theta)³

= sin^6theta + cos^6theta + 3sin²theta.cos²theta(sin²theta + cos²theta)

1 = sin^6theta + cos^6theta + 3sin²theta.cos²theta

sin^6theta + cos^6theta

= 1 - 3sin²theta.cos²theta

sin^6theta + cos^6theta -1

= - 3sin²theta.cos²theta

compare this to the question....

we get lambda = -3