Question

If cosec theta=2, show that cot theta+sin theta/1+cos theta=2

Answer 1

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Answer 2

Trigonometry: Trigonometry is the study of angles and relations between angles and their sin, cos, tan, cosec, sec, cot ratios. There are many formulae for calculations:

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin2A = 2 sinA cosA

• cos2A = cos²A - sin²A

• tan2A = 2 tanA / (1 - tan²A)

• cosec(π/6) = 2

Proof:

Given,

cosecθ = 2

or, cosecθ = cosec(π/6)

Then θ = π/6

L.H.S. = cotθ + sinθ/(1 + cosθ)

= cot(π/6) + {sin(π/6)}/{1 + cos(π/6)}

= √3 + (1/2)/{1 + (√3)/2}

= √3 + 1/(2 + √3)

= (2√3 + 3 + 1)/(2 + √3)

= (4 + 2√3)/(2 + √3)

= 2 (2 + √3)/(2 + √3)

= 2 = R.H.S.

∴ cotθ + sinθ/(1 + cosθ) = 2, where cosecθ = 2

Hence proved.