Question

Q 22: If ѕіn Ө+ cos Ө= 1, then
the value of sin 20 is equal to
1/2
ОООО
1​

Answer 1

Answer:

cos 20° – sin 20° = p

Squaring on both sides,

cos2(20°) + sin2(20°) – 2 sin 20° cos 20° = p2

1 – sin 2(20°) = p2

sin 40° = 1 – p2

Now,

cos 40° = √[1 – sin2(40°)]

= [√1 – (1 – p2)2]

= √[1 – (1 + p4 – 2p2)]

= √(2p2 – p4)

= √[p2(2 – p2)]

= p√(2 – p2)