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If θ = 45°, what is the value of $cos 2 θ − sin 2 θ$ ?

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sin θ

None of the above.

answer is B.

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Detailed Solution

Given that

θ = 45 °

.
We have to find the value of

cos 2 θ − sin 2 θ

.
We know that,

sin 45 ° = 12

cos 45 ° = 12

Putting the value of trigonometric functions for given angles in the expression,

⇒ cos 2 θ − sin 2 θ = cos 2 45 ° − sin 2 45 °

⇒ cos 2 θ − sin 2 θ = 122 − 122

⇒ cos 2 θ − sin 2 θ = 12 − 12

⇒ cos 2 θ − sin 2 θ = 0

Thus, the value of

cos 2 θ − sin 2 θ

when

θ = 45 °

is 0.
Thus, option 2 is correct.

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