Question

if cos A=3/5,then write the value of sin 2A​

Answer 1

Solution :-

Given ,

• cosA = 3/5

We need to find ,

• sin2A

Firstly finding the opposite side of angle A

So , using Pythagoras theorem ,

→ Hypotenuse² = Base² + Height²

→ 5² = Base² + 3²

→ 25 - 9 = Base²

→ Base = √16

→ Base = 4

Now finding , sinA

→ sinA = Opposite/Hypotenuse

→ sinA = 4/5

Now finding , sin2A

As we know that ,

♦ sin2A = 2sinAcosA

♦ sin2A = 2 × ( 4/5 ) × ( 3/5 )

♦ sin2A = 24/25

Hence , sin2A = 24/25

Answer 2

Solution :

Given ,

• cosA = 3/5

We need to find ,

• sin2A

Firstly finding the opposite side of angle A

So , using Pythagoras theorem ,

→ Hypotenuse² = Base² + Height²

→ 5² = Base² + 3²

→ 25 - 9 = Base²

→ Base = √16

→ Base = 4

Now finding , sinA

→ sinA = Opposite/Hypotenuse

→ sinA = 4/5

Now finding , sin2A

As we know that ,

♦ sin2A = 2sinAcosA

♦ sin2A = 2 × ( 4/5 ) × ( 3/5 )

♦ sin2A = 24/25

Hence , sin2A = 24/25

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