Question

Sec theeta + tan theeta= p. Show that sin theeta=p^2 -1/p^2+1

Answer 1

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Answer 2

S.ec + tan = p

(S.ec + tan)² =p²

S.ec² + 2.S.ec.tan + tan² = p²

1/cos² +2(1/cos)(sin/cos) + sin²/cos² = p²

(1 + 2.sin + sin²)/cos² = p²

(1 + sin)²/cos² = p²

(1 + sin)²/1 - sin² = p²

(1 + sin)²/(1 - sin)(1 + sin) = p²

(1 + sin)/(1 - sin) = p²

1 + sin = p²(1 - sin)

1 + sin = p² - p²sin

p² - 1 = p²sin + sin

p² - 1 = sin(p² + 1)

sin = (p² - 1)/(p² + 1))

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