Question

Q
If sin theta=1, then cos 2theta=
2)1
110
3)-1
4)2
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Answer 1

Answer:

Let sin theta be p/h .

Therefore,

p/h=1.

Let p=h=x .

By pythagoras theorem,

b=h-p=x-x=0.

Now, cos theta = b/h = 0/1 = 0

the correct answer is 0 .

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Answer 2

Given :

$\sf sin \theta = 1$

To find :

$\sf the \: value \: of \: cos 2\theta$

Formula used :

$\underline{ \boxed{ \rm \large cos \: 2x = {cos}^{2} x - {sin}^{2} x}}$

Solution :

$\sf \implies sin \theta = 1 \\ \sf \: then \: \theta \: must \: be \: 90 \degree$

$\implies \sf cos \: 2 \theta = {cos}^{2}\theta - {sin}^{2} \theta$

$\sf\implies cos \: 2 \theta = {cos}^{2} 90 \degree- {sin}^{2} 90 \degree$

we know that :-

• cos 90° = 0
• sin 90° = 1

$\sf\implies cos \: 2 \theta = 0- 1$

$\sf\implies cos \: 2 \theta = - 1$

Answer :

• option (3)-1 is correct