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Question

If secθ+tanθ=p then sinθ=p2+1p21

A
True
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B
False
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Solution

The correct option is B False
secθ+tanθ=p .........(1)
(secθ+tanθ)(secθtanθ)=p(secθtanθ)
sec2θtan2θ=p(secθtanθ)
1=p(secθtanθ) since sec2θtan2θ=1
secθtanθ=1p ......(2)
Adding (1) and (2) we get
secθ+tanθ+secθtanθ=p+1p
2secθ=p2+1p
secθ=p2+12p
Equations (1)(2) we get
secθ+tanθsecθ+tanθ=p1p
2tanθ=p21p
tanθ=p212p
Now tanθsecθ=p212pp2+12p=p21p2+1
sinθcosθ×cosθ=p21p2+1
sinθ=p21p2+1

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