Question

12. If A = 45°, verify that:
(i) sin 2A = 2 sin Acos A​

Answer 1

Given :-

• A = 45°

To Prove that :-

• $sin \: 2a = 2sin \: a \: cos \: a$

Solution :-

$: \implies \: sin \: 2a = 2sin \: a \: cos \: a$

Putting the value of a →

$: \implies \: sin \: (2 \times 45) = 2 \times sin \: 45 \times cos \: 45 \\ \\ : \implies \: sin \: 90 = 2 \times sin \: 45 \times cos \: 45$

We know that :-

• $sin \: 90 = 1$
• $sin \: 45 = \frac{1}{ \sqrt{2} }$
• $cos \: 45 = \frac{1}{ \sqrt{2} }$

So,

$: \implies1 = 2 \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } \\ \\ : \implies1 = 2 \times \frac{1}{2} \\ \\ : \implies1 = 1 \\ \\ l.h.s. = r.h.s.$

Hence proved !!

Answer 2

Answer:

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