What will we get when we simplify -1-sin2A - A-

From Trigonometric identity, sin^2A + cos^2A = 1 nbsp; ⇒ 1 sin^2A nbsp; = cos^2A ∴ nbsp; √(1 sin^2A)/ A=√(cos^2A)/ A = nbsp;cos A/cos A/sin A = sin A ...

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Standard X

Mathematics

Trigonometric Identity- 1

What will we ...

Question

What will we get when we simplify $\frac{\sqrt{1 - {sin}^{2} A}}{cot A}$ ?

cot A

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sin A

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cos A

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tan A

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Solution

The correct option is B $sin A$
From Trigonometric identity,
${sin}^{2} A + {cos}^{2} A = 1$
$\Rightarrow$ $1 - {sin}^{2} A = {cos}^{2} A$

$∴$ $\frac{\sqrt{1 - {sin}^{2} A}}{cot A} = \frac{\sqrt{{cos}^{2} A}}{cot A}$

= $\frac{cos A}{\frac{cos A}{sin A}}$

= $sin A$

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What will we get when we simplify √1−sin2AcotA?

The correct option is B sinAFrom Trigonometric identity, sin2A+cos2A=1 ⇒ 1−sin2A=cos2A ∴ √1−sin2AcotA=√cos2AcotA = cosAcosAsinA = sinA

What will we get when we simplify $\frac{\sqrt{1 - {sin}^{2} A}}{cot A}$ ?

The correct option is B $sin A$
From Trigonometric identity,
${sin}^{2} A + {cos}^{2} A = 1$
$\Rightarrow$ $1 - {sin}^{2} A = {cos}^{2} A$

$∴$ $\frac{\sqrt{1 - {sin}^{2} A}}{cot A} = \frac{\sqrt{{cos}^{2} A}}{cot A}$

= $\frac{cos A}{\frac{cos A}{sin A}}$

= $sin A$