Question

Prove that
(i) 1 + cos 2A = cot A sin 2A​

Answer 1

Answer:

Step by step explanation:

cos2A can be written as 2cos²A-1

plugging that value in question we get

2cos²A now multiplying and dividing with sinA we get

2cosA*sinA(cosA/sinA)

2sinA*cosA=sin2A and cosA/sinA=cotA

we finally get

cotA*sin2A

I REALLY HOPE THIS HELPS YOU

Answer 2

1 + cos 2A = cot A sin 2A is proved

Given :

The expression 1 + cos 2A = cot A sin 2A

To find :

To prove the expression

Formula Used :

1. cos 2A = 2cos²A - 1

2. sin 2A = 2 sin A cos A

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

1 + cos 2A = cot A sin 2A

Step 2 of 2 :

Prove the expression

RHS

$\displaystyle \sf = cot A \: sin 2A$

$\displaystyle \sf = \frac{cosA}{sinA} \times 2 \: sinA \: cosA$

$\displaystyle \sf = 2 {cos }^{2} A$

$\displaystyle \sf = 1 + {cos }^{} \: 2A\: \: \: \bigg[ \: \because \: 2 {cos }^{2} A - 1 = {cos }^{} \: 2A \bigg]$

= LHS

Hence the proof follows

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