Question

If secant theta + tan theta is equal to p then prove that sin theta is equal to p square minus 1 by p square + 1

Answer 1

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given : secθ + tanθ = p ----(1)

we know that sec²θ-tan²θ = 1

(secθ-tanθ) (secθ-tanθ) = 1

p (secθ-tanθ) = 1

secθ-tanθ = 1/p ----(2)

Adding ---(1) and ------(2) we get,

2 secθ = p²+1 / p -----(3)

EQUATION (1) - (2)

2tanθ = p²-1 / p ---(4)

EQUATION 3/4

2 secθ/ 2tanθ = p²+1/p / p²-1/p

secθ/tanθ = p²+1 / p²-1

1/cosθ /  sinθ/cosθ  =  p²+1/ p²-1

1/sinθ = p²+1/ p²-1

sinθ = p²-1 /  p²+1

HENCE PROVED !!

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