Question

sin 135º - cos 240°
÷
sin 135º+cos 240°
= a + Vā, then b=
​

Answer 1

Step-by-step explanation:

sin 135° = sin(90+45) = cos 45° = 1/√2

cos 240° = cos(180+60) = - cos 60° = -1/2

sin 135º - cos 240° = 1/√2 - ( -1/2 ) = 2+√2 / 2√2

sin 135º+cos 240° = 1/√2 + ( -1/2 ) = 2-√2 / 2√2

sin 135º - cos 240° ÷ sin 135º+cos 240° = a + √b

=> 2+√2 / 2√2 ÷ 2-√2 / 2√2 = a + √b

=> 2+√2 / 2-√2 = a + √b

Rationalising the denominator in LHS,

=> (2+√2)² / (2-√2)(2+√2) = a + √b

=> 4+2+4√2 / 4-2 = a + √b

=> 6+4√2 / 2 = a + √b

=> 2(3+2√2) / 2 = a + √b

=> 3+2√2 = a + √b

=> 3+√8 = a + √b

comparing like terms,

.•. a = 3 and b = 8