Question

tan 45 + sin45 upon
tan45 - sin 45​

Answer 1

Answer:

tan45 + sin45/ tan 45 - sin 45

=( 1+ 1/√2). / (1-1√2)

= √2+1 / √2-1

Answer 2

★ Solution :-

tan45° + sin45°/tan45° - sin45°

As we know that,

• tan45° = 1

• sin45° = 1/√2

Substituting we have,

→ [ 1 + ( 1/√2 ) ]/[ 1 - ( 1/√2 ) ]

→ [ ( √2 + 1 )/√2 ]/[ ( √2 - 1 )/√2 ]

→ [ √2 + 1 ]/[ √2 - 1 ]

By Rationalizing the denominator,

→ [ √2 + 1/√2 - 1 ] × [ √2 + 1/√2 + 1 ]

Using ,

• ( a + b)(a + b) = ( a + b)² = a² + b² + 2ab

• (a + b)(a - b) = a² - b²

→ ( √2 + 1 )²/( √2 )² - (1)²

→ ( √2 )² + 1² + 2(√2)(1)/2 - 1

→ 2 + 1 + 2√2/1

→ 3 + 2√2

Hence , tan45° + sin45° ÷ tan45° - sin45° = 3 + 2√2.