Prove the identity- - 2-cosec2-cosec-4 MARKS -

Formula: 2 Marks Proof: 2 Marks LHS=√(sec^2 θ+cosec^2 θ)=√(1/cos^2 θ+1/sin^2 θ)=√(sin^2 θ+cos^2 θ/cos^2 θ sin^2 θ) =√(1/cos^2 θ sin^2 θ)=√(sec^2 θ cosec^2 θ) ...

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Standard X

Mathematics

Trigonometric Identities

Prove the ide...

Question

Prove the identity: $\sqrt{s e c^{2} θ + c o s e c^{2} θ} = s e c θ c o s e c θ$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks
$L H S = \sqrt{s e c^{2} θ + c o s e c^{2} θ} = \sqrt{\frac{1}{c o s^{2} θ} + \frac{1}{s i n^{2} θ}} = \sqrt{\frac{s i n^{2} θ + c o s^{2} θ}{c o s^{2} θ s i n^{2} θ}} = \sqrt{\frac{1}{c o s^{2} θ s i n^{2} θ}} = \sqrt{s e c^{2} θ c o s e c^{2} θ} = s e c θ c o s e c θ = R H S$

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Prove the identity: √sec2 θ+cosec2 θ=sec θ cosec θ [4 MARKS]

Formula: 2 Marks Proof: 2 Marks LHS=√sec2 θ+cosec2 θ=√1cos2 θ+1sin2 θ=√sin2 θ+cos2 θcos2 θ sin2 θ=√1cos2 θ sin2 θ=√sec2 θ cosec2 θ=sec θ cosec θ=RHS

Prove the identity: $\sqrt{s e c^{2} θ + c o s e c^{2} θ} = s e c θ c o s e c θ$ [4 MARKS]