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Question

(secθcosθ)2+(cosecθsinθ)2(cotθtanθ)2=

[1 mark]

A
-1
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B
1
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C
0
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D
2
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Solution

The correct option is B 1
(secθcosθ)2=sec2θ+cos2θ2(secθ)(cosθ)(cossecθsinθ)2=cosec2θ+sin2θ2(cosecθ)(sinθ)(cotθtanθ)2=cot2θ+tan2θ2(cotθ)(tanθ)(secθcosθ)2+(cosecθsinθ)2(cotθtanθ)2=(sec2θ+cos2θ2)+(cosec2θ+sin2θ2)(cot2θ+tan2θ2)

In the RHS of the equation,

(secθ)(cosθ)=1, (cosecθ)(sinθ)=1 and (cotθ)(tanθ)=1

(secθcosθ)2+(cosecθsinθ)2(cotθtanθ)2=(sec2θtan2θ)+(sin2θ +cos2θ)+(cosec2θcot2θ)22+2

(sec2θtan2θ) =1, (sin2θ +cos2θ)=1 and (cosec2θcot2θ)=1

(secθcosθ)2+(cosecθsinθ)2(cotθtanθ)2 =1+1+1 2

(secθcosθ)2+(cosecθsinθ)2(cotθtanθ)2=1

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