Prove that-1-sin-1-sin-1-sin-1-sin-2 - -2 MARKS-

Concept: 1 Mark Applicaiton: 2 Mark We have =√(1+sin θ)/√(1 sin θ)+√(1 sin θ)/√(1+sin θ) =1+sin θ+1 sin θ/√((1 sin θ)(1+sin θ)) =2/√((1 sin^2 θ)) =2/√(co ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Prove that√1+...

Question

Prove that

$\sqrt{\frac{1 + s i n θ}{1 - s i n θ}} + \sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = 2 s e c θ$ [2 MARKS]

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Solution

Concept: 1 Mark
Applicaiton: 2 Mark

We have

$= \frac{\sqrt{1 + s i n θ}}{\sqrt{1 - s i n θ}} + \frac{\sqrt{1 - s i n θ}}{\sqrt{1 + s i n θ}}$

$= \frac{1 + s i n θ + 1 - s i n θ}{\sqrt{(1 - s i n θ) (1 + s i n θ)}}$

$= \frac{2}{\sqrt{(1 - s i n^{2} θ)}}$

$= \frac{2}{\sqrt{c o s^{2} θ}}$

$= \frac{2}{c o s θ}$

$= 2 s e c θ$

$∴$ LHS = RHS

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Prove that √1+sin θ1−sin θ+√1−sin θ1+sin θ=2 sec θ [2 MARKS]

Concept: 1 Mark Applicaiton: 2 Mark We have =√1+sin θ√1−sin θ+√1−sin θ√1+sin θ =1+sin θ+1−sin θ√(1−sin θ)(1+sin θ) =2√(1−sin2 θ) =2√cos2 θ =2cos θ =2 sec θ ∴ LHS = RHS

Prove that

$\sqrt{\frac{1 + s i n θ}{1 - s i n θ}} + \sqrt{\frac{1 - s i n θ}{1 + s i n θ}} = 2 s e c θ$ [2 MARKS]