The numerical value of cosec -1-cos-sin-sin-1-cos-22- is

Cosec θ[1 cosθsinθ+sinθ1 cosθ] 2^2θ = nbsp;[1 cosθsin^2 θ+11 cosθ] 2^2θ = nbsp;[1 cosθ1 cos^2θ+11 cosθ] 2^2θ = nbsp;[11+cosθ+11 cosθ] 2^2θ = nbsp;[1 ...

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Standard XI

Mathematics

Trigonometric Ratios of Common Angles

The numerical...

Question

The numerical value of $cosec θ [\frac{1 - cos θ}{sin θ} + \frac{sin θ}{1 - cos θ}] - 2 {cot}^{2} θ$ is

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Solution

The correct option is C $2$
$cosec θ [\frac{1 - cos θ}{sin θ} + \frac{sin θ}{1 - cos θ}] - 2 {cot}^{2} θ = [\frac{1 - cos θ}{{sin}^{2} θ} + \frac{1}{1 - cos θ}] - 2 {cot}^{2} θ = [\frac{1 - cos θ}{1 - {cos}^{2} θ} + \frac{1}{1 - cos θ}] - 2 {cot}^{2} θ = [\frac{1}{1 + cos θ} + \frac{1}{1 - cos θ}] - 2 {cot}^{2} θ = [\frac{1 + cos θ + 1 - cos θ}{1 - {cos}^{2} θ}] - 2 {cot}^{2} θ = 2 {cosec}^{2} θ - 2 {cot}^{2} θ = 2$

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The numerical value of cosec θ[1−cosθsinθ+sinθ1−cosθ]−2cot2θ is

The correct option is C 2cosec θ[1−cosθsinθ+sinθ1−cosθ]−2cot2θ=[1−cosθsin2θ+11−cosθ]−2cot2θ=[1−cosθ1−cos2θ+11−cosθ]−2cot2θ=[11+cosθ+11−cosθ]−2cot2θ=[1+cosθ+1−cosθ1−cos2θ]−2cot2θ=2 cosec 2θ−2cot2θ=2

The numerical value of $cosec θ [\frac{1 - cos θ}{sin θ} + \frac{sin θ}{1 - cos θ}] - 2 {cot}^{2} θ$ is