The correct option is A 1We know that, sinθ× cosecθ = 1 and cosθ× secθ = 1. Hence, sinθ× cosθ× cosecθ× secθ = sinθ× cosecθ nbsp;× cosθ nbsp;× secθ = 1 × 1 ...

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Sine Rule

sinθ×cosθ×cos...

Question

$s i n θ \times c o s θ \times c o s e c θ \times s e c θ$ = .

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t a n θ

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c o t θ

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Solution

The correct option is A 1
We know that,
$s i n θ \times c o s e c θ = 1$
$and c o s θ \times s e c θ = 1$ .

Hence,
$s i n θ \times c o s θ \times c o s e c θ \times s e c θ$
$= s i n θ \times c o s e c θ \times c o s θ \times s e c θ$
$= 1 \times 1 = 1$

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Similar questions

Q. If

\frac{cosec θ + cot θ}{cosec θ - cot θ} = \frac{81}{49}

, then find

\frac{cos θ + sin θ}{sin θ - cos θ}

\frac{cos θ - sin θ + 1}{cos θ + sin θ - 1} = cosec θ + cot θ

Prove the following trigonometric identities.
(i) $\frac{1 + cos θ + sin θ}{1 + cos θ - sin θ} = \frac{1 + sin θ}{cos θ}$

(ii) $\frac{sin θ - cos θ + 1}{sin θ + cos θ - 1} = \frac{1}{sec θ - tan θ}$

(iii) $\frac{cos θ - sin θ + 1}{cos θ + sin θ - 1} = cosec θ + cot θ$

(iv) $(sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ$

Q. Prove that

\frac{sin θ}{1 - cos θ} = c o s e c θ + cot θ

Q. Solve the following equations:
(i)

\sin θ + \cos θ = \sqrt{2}

(ii)

\sqrt{3} \cos θ + \sin θ = 1

(iii)

\sin θ + \cos θ = 1

(iv)

cosec θ = 1 + \cot θ

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sinθ×cosθ×cosecθ×secθ = .

The correct option is A 1We know that, sinθ×cosecθ=1 and cosθ×secθ=1. Hence, sinθ×cosθ×cosecθ×secθ =sinθ×cosecθ×cosθ×secθ =1×1=1

$s i n θ \times c o s θ \times c o s e c θ \times s e c θ$ = .

The correct option is A 1
We know that,
$s i n θ \times c o s e c θ = 1$
$and c o s θ \times s e c θ = 1$ .

Hence,
$s i n θ \times c o s θ \times c o s e c θ \times s e c θ$
$= s i n θ \times c o s e c θ \times c o s θ \times s e c θ$
$= 1 \times 1 = 1$