Prove that :sin240o+sin250o=1

Taking LHS= sin240o+sin250o⇒ cos2 (90° - 40°) + sin2 50° [∵ Sin θ = cos (90° - θ)]⇒ cos2 50° + sin2 50°= 1 =RHS [∵ cos2 θ + sin2 θ = 1]Hence Proved

Q21 of 268 Page 4

Prove that :
sin²40^o+sin²50^o=1

Taking LHS= sin²40^o+sin²50^o

⇒ cos² (90° - 40°) + sin² 50° [∵ Sin θ = cos (90° - θ)]

⇒ cos² 50° + sin² 50°

= 1 =RHS [∵ cos² θ + sin² θ = 1]

Hence Proved

Prove that :

sin 54^o+cos67^o= sin23^o+cos36^o

Prove that :

cos 27+ sin51^o = sin63^o+cos 39^o

Prove that :

sin²29^o + sin²61^o=1

Prove that :

sin θ .cos (90° - θ) + cos θ sin (90° - θ).