Question

16. If sin 0 = 1, then the value of sin 20 is
(a)-1
(b) 0
(c)1
(d) 2​

Answer 1

SOLUTION

CORRECT QUESTION

TO DETERMINE

If sin θ = 1 then the value of sin 2θ is

(a) - 1

(b) 0

(c) 1

(d) 2

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula

$\sf sin 2 \theta = 2 sin\theta \: cos\theta$

EVALUATION

Here it is given that

$\sf sin \theta = 1$

Now we have

$\sf sin 2 \theta$

$\sf = 2 sin\theta \: cos\theta$

$\sf = 2 sin\theta \: \sqrt{1 - { sin}^{2}\theta }$

$\sf = 2 \times 1 \times \: \sqrt{1 - { 1}^{2} }$

$\sf = 2 \times 1 \times \: \sqrt{1 - 1 }$

$\sf = 2 \times 1 \times 0$

$\sf =0$

FINAL ANSWER

Hence the correct option is (b) 0

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