Question

If tan A = √2-1. Find sin Ax Cos A​

Answer 1

Answer:

Hey mate ! Your answer is √2/4 .

Explanation:

Tan A = √2 - 1

Tan A = opposite / adjacent (i.e) tan a = o / a

(√ 2 - 1 ) / 1 = o / a  ( o = √2 - 1 , a = 1 )

By pythagoras theorem ,

o² + a² = h² (where h is the hypotenuse)

(√2 - 1 )² + (1)² = h²

2 + 1 - 2√2 + 1 = h ²

h² = [4 - 2√2 ]

Sin A = o / h , Cos A = a / h

Sin A × Cos A = ( o × a ) / h²

                       = (√ 2 - 1 ) / ( 4 - 2 √2)

Rationalizing the Denominator,

⇒ [( √ 2 - 1 ) × ( 4 + 2 √2 )] / [( 4 - 2 √2 )(4 + 2 √2)]

⇒ (4 √2 + 4 - 4 - 2√2 ) / ( 16 - 8 )

⇒ (2 √2) / 8

⇒ √2 / 4

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