Question

If TanTheta =1/2 then evaluate (costheta/sintheta+sinthetha/1+costheta)
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Answer 1

tan¢ = 1/2

Thus, in the form of a triangle it will be

P (perpendicular) = 1 and B (base) = 2

Thus, (Hypotenuse)² = P² + B²

=> H² = 1 + 4

=> H = √5

Thus, sin¢ = 1/√5 and cos¢ = 2/√5

Thus in the problem above we see that,

cos¢/sin¢ = cot¢ = 2

sin¢/1 + cos¢

= (1/√5)/(1 + 2/√5)

= (1/√5)/[(√5 + 2)/√5]

= 1/(√5 + 2)

Hence the solution is 2 + 1/(√5 + 2)

= (2√5 + 5)/(√5 + 2)

= (2√5 + 5)(√5 + 2)/(5 - 4)

= 10 + 4√5 + 5√5 +10

= (20 + 9√5)

Thus the answer is (20 + 9√5).

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