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The value of ^{3} ( 1+ )+ ^{3} ( 1+ ) is equal to

Question

The value of $sin^{3} α (1 + cot α) + cos^{3} α (1 + tan α)$ is equal to

sin α - cos α

sin α + cos α

sin α cos α

co sec α sec α

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Evelyn Discussed

The value of

sin^{3} α (1 + cot α) + cos^{3} α (1 + tan α)

is equal to

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Text solutionVerified

Given expression

= sin^{3} α (1 + \frac{cos α}{sin α}) + cos^{3} α (1 + \frac{sin α}{cos α})

= sin^{2} α (sin α + cos α) + cos^{2} α

(cos α + sin α)

= (cos α + sin α) (sin^{2} α + cos^{2} α)

= sin α + cos α

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Question Text	The value of $sin^{3} α (1 + cot α) + cos^{3} α (1 + tan α)$ is equal to
Answer Type	Text solution:1
Upvotes	150