Question

cosA = cotA/√(1+cot2A)
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Answer 1

Answer:

Step-by-step explanation:

1+cot= csc

1+cot^2=csc^2

√(csc^2)= csc

cotA/cscA = cos/sin / 1/sin

cos/sin * sin = cos

cos=cos

Answer 2

Correct Question:

Prove that $cosA = \frac{cotA}{\sqrt{(1+cot^2A)}}$.

Final Answer:

The value of the expression $\frac{cotA}{\sqrt{(1+cot^2A)}}$ is proved to be equal to cos A.

Given:

The provide trigonometric identity is $cosA = \frac{cotA}{\sqrt{(1+cot^2A)}}$.

To Find:

The value of the expression $\frac{cotA}{\sqrt{(1+cot^2A)}}$ is $=cosA$ is to be proved .

Explanation:

The following formulae are needed for solving the present problem.

• The formula linking the trigonometric terms of cosec and cot is $cosec^2P = 1+cot^2P$
• The trigonometric function cosec is the reciprocal of the  trigonometric function sin.
• The trigonometric function sec is the reciprocal of the  trigonometric function cos.
• The trigonometric function cot is equal to the trigonometric function cos divided by the trigonometric function sin.
• The trigonometric function tan is equal to the trigonometric function sin divided by the trigonometric function cos.

Step 1 of 3

Simplify the Right Hand Side (RHS) of the identity in the given problem in the following way using $cosec^2A = 1+cot^2A$.

$\frac{cotA}{\sqrt{(1+cot^2A)}}\\= \frac{cotA}{\sqrt{cosec^2A}}\\ = \frac{cotA}{cosecA}$

Step 2 of 3

Simplify further the above expression using the equivalent trigonometric terms in the following way.

$\frac{cotA}{cosecA}\\\\= \frac{\frac{cosA}{sinA} }{\frac{1}{sinA} }\\\\=\frac{cosA}{sinA}\times {\frac{sinA} {1}}$

Step 3 of 3

Now, cancelling the common trigonometric terms in the above expression, the following is achieved.

$\frac{cosA}{sinA}\times {\frac{sinA} {1}}\\\\=cosA\;\;\;\;[as\;sinA\ne0]$

So it is evident that it equal to  the Left Hand Side (LHS) of the stated expression.

Therefore, the required proof is $cosA = \frac{cotA}{\sqrt{(1+cot^2A)}}$.

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