Question

If 2 sin (2x) = √3, then find the value of sin²( 2 x ) + tan ²(x ) .

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Answer 1

Answer:

13/12

Step-by-step explanation:

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Answer 2

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★ Solution :-

2sin( 2x ) = √3

Simplifying

➮ sin( 2x ) = √3/2

Here , by comparing with sin60° = √3/2 we have ,

➮ 2x = 60°

➮ x = 60°/2

➮ x = 30°

Now , finding sin²( 2x ) + tan²( x )

➮ [ sin( x ) ]² + [ tan²( x ) ]

Now , substituting x = 30°

➮ { sin[ 2 ( 30° ) ] }² + tan²30°

➮ [ sin60° ]² + ( 1/√3 )²

➮ [ √3/2 ]² + ( 1/√3 )²

➮ ( √3 )²/2² + 1²/(√3)²

➮ 3/4+ 1/3

➮ 13/12

Hence , sin²( 2x ) + tan²( x ) = 7/3

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