Question

if tan a=2 and a belongs to (π,3π/2) then the value of the expression cos a/sin^3a+cos^3a is equal to

Answer 1

Step-by-step explanation:

TanA=2

so by Pythagoras theorem

SinA=2/√5

SinA=2/√5CosA=1/√5

So in the question

CosA/sin³A+cos³A. from[a³+b³=(a+b)(a²-2ab+b²)]

=cosA/(sinA+CosA) (sin²A+cosA²-2sinACosA)

=CosA/(sinA+cosA)(1-2sinAcosA)

now by substituting the values

(1/√5)

[(2/√5)+(1/√5)][1-2*(2/√5)*(1/√5)

1

(√5)(3/√5) [(5-4)/5]

1

3* 1/5

5.

3

Thank you

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