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Calculate , { , }{^3 , , + , ^3 , } if =2.

Question

Calculate
$\frac{sin α}{sin ^{3} α + cos ^{3} α}$ if $tan$ $α$ =2.

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Chloe Discussed

Calculate

\frac{sin α}{sin ^{3} α + cos ^{3} α}

if

tan

α

=2.

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

For such kind of question we have to just simplify the question as much possible, so first we take common

(cos α)^{3}

from denominator and then we got

\frac{tan α \times ( sec α ) ^{2}}{1 + ( tan α ) ^{3}}

and using trignometric relation we convert sec into tan after that

\frac{tan α \times ( 1 + ( tan α ) ^{2} )}{1 + ( tan α ) ^{3}}

and as given the value of

tan α

put this and solve simple calculation we got the value of expression is equal to

\frac{10}{9}

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Question Text	Calculate $\frac{sin α}{sin ^{3} α + cos ^{3} α}$ if $tan$ $α$ =2.
Answer Type	Text solution:1
Upvotes	150