Simplify the expressioncosec2-1 - 2-1

The correct option is A 1We know that cosec^2 θ 1 = cot^2 θ and sec^2 θ 1 = tan^2 θ ∴(cosec^2 θ 1) × (sec^2 θ 1) = cot^2 θ× tan^2 θ = cot^2 θ×1/cot^2 θ ...

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Standard X

Mathematics

Trigonometric Identities

Simplify the ...

Question

Simplify the expression-
$(c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)$

c o t^{2} θ

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t a n^{2} θ

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Solution

The correct option is C $1$
We know that $c o s e c^{2} θ - 1 = c o t^{2} θ$ and $s e c^{2} θ - 1 = t a n^{2} θ$
$∴ (c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)$
$= c o t^{2} θ \times t a n^{2} θ$
$= c o t^{2} θ \times \frac{1}{c o t^{2} θ}$
$= 1$ .

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Similar questions

Simplify the expression-
$(c o s e c^{2} θ - 1) \times ({sec}^{2} θ - 1)$

Q. Simplify the expression -

(c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)

Q. Simplify :

(1 - cos θ) (1 + cos θ) (1 + {cot}^{2} θ)

$\frac{t a n^{2} θ}{(1 + t a n^{2} θ)} + \frac{c o t^{2} θ}{(1 + c o t^{2} θ)} = 1$

Q. Solve

(\frac{4}{{sec}^{2} θ} + \frac{1}{1 + {cot}^{2} θ} + 3 {sin}^{2} θ)

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Simplify the expression- (cosec2θ−1)×(sec2θ−1)

The correct option is C 1We know that cosec2θ−1=cot2θ and sec2θ−1=tan2θ ∴(cosec2θ−1)×(sec2θ−1) =cot2θ×tan2θ =cot2θ×1cot2θ =1.

Simplify the expression-
$(c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)$

The correct option is C $1$
We know that $c o s e c^{2} θ - 1 = c o t^{2} θ$ and $s e c^{2} θ - 1 = t a n^{2} θ$
$∴ (c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)$
$= c o t^{2} θ \times t a n^{2} θ$
$= c o t^{2} θ \times \frac{1}{c o t^{2} θ}$
$= 1$ .