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Solve: { { +1}{ -1}}= +

Question

Solve:
$\frac{sec θ + 1}{sec θ - 1} = cot θ + csc θ$

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Solve:

\frac{sec θ + 1}{sec θ - 1} = cot θ + csc θ

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Text solutionVerified

L . H . S = \frac{sec θ + 1}{sec θ - 1}

= \frac{\frac{1}{cos θ} + 1}{\frac{1}{cos θ} - 1} = \frac{1 + cos θ}{1 - cos θ}

Multiply numerator and denominator by

(1 + cos θ)

= \frac{( 1 + cos θ ) ( 1 + cos θ )}{( 1 - cos θ ) ( 1 + cos θ )}

= \frac{( 1 + cos θ ) ^{2}}{1 - cos ^{2} θ}

= \frac{( 1 + cos θ ) ^{2}}{sin ^{2} θ}

= \frac{1 + cos θ}{sin θ}

= \frac{1}{sin θ} + \frac{cos θ}{sin θ}

csc θ + cot θ

or

cot θ + csc θ

R . H . S

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Question Text	Solve: $\frac{sec θ + 1}{sec θ - 1} = cot θ + csc θ$
Answer Type	Text solution:1
Upvotes	150