If - is in the first quadrant- then -1-sin 2 -cos-

The correct option is B False The term under square root is always positive ⇒ L.H.S is always positive But, R.H.S is negative So, the statement is not true fo ...

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Standard X

Mathematics

Complementary Trigonometric Ratios

If θ is in th...

Question

If $θ$ is in the first quadrant, then $\sqrt{(1 - sin 2 θ)} = - cos θ$

True

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False

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Solution

The correct option is B
False

The term under square root is always positive

$\Rightarrow$ L.H.S is always positive

But, R.H.S is negative

So, the statement is not true for any value of $θ$ in the first quadrant.

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If θ is in the first quadrant, then √(1−sin2θ)=−cosθ

The correct option is B False The term under square root is always positive ⇒ L.H.S is always positive But, R.H.S is negative So, the statement is not true for any value of θ in the first quadrant.

If $θ$ is in the first quadrant, then $\sqrt{(1 - sin 2 θ)} = - cos θ$

The correct option is B
False

The term under square root is always positive

$\Rightarrow$ L.H.S is always positive

But, R.H.S is negative

So, the statement is not true for any value of $θ$ in the first quadrant.