Question

If sin thita =A and sin square thita =B, find the expression for cos thita in terms of a and b. Hence find a relation between a and b not involving thita​

Answer 1

Answer:

I am taking Theta to be 'A'

According to the Question,

⇒ Sin A = a

⇒ Sin 2A = b

We need to find Cos A in terms of a and b.

According to trigonometric identity,

⇒ Sin 2A = 2 × Sin A × Cos A

Substituting the values we get,

⇒ b = 2 × a × Cos A

⇒ Cos A = b / 2a

We know that,

⇒ Sin²A + Cos²A = 1   [ Trigonometric Identity ]

⇒ a² + ( b / 2a )² = 1

⇒ a² + b² / 4a² = 1

Taking LCM we get,

⇒ ( 4a⁴ + b² ) / 4a² = 1

⇒ 4a⁴ + b² = 4a²   [ Cross multiplying the denominator ]

⇒ 4a⁴ - 4a² = -b²

⇒ 4a² ( a² - 1 ) = -b²

⇒ 4a² ( 1 - a² ) = b²

⇒ √ ( 4a² ( 1 - a² )) = √ b²

⇒ 2a √ ( 1 - a² ) = b

This is the required relation.

Hope it helped !!

Have a great day :)

Answer 2

Answer:

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Thanks .