show that cos 2 (45 + theta) + cos 2 (45 - theta) / tan (60 + theta) tan (30 - Maths - Introduction to Trigonometry

Question

show that cos 2 (45 + theta) + cos 2 (45 - theta) / tan (60 +
theta) tan (30 - theta) = 1

Sandeep Kumar · Answer

cos2(45 + theta) + cos2(45 - theta) /
tan(60 + theta) tan(30 - theta) = 1
LHS =cos2(45 + theta) + sin2{90 - (45
-theta)} / tan(60 + theta) cot{90 - (30 - theta)}
=cos2(45 + theta) + sin2(90 - 45 + theta)
/ tan(60 + theta) cot(90 - 30 + theta)
=cos2(45 + theta) + sin2(45 + theta) /
tan(60 + theta) cot(60 + theta)
= 1 / 1
LHS = 1 = RHS

show that cos 2 (45 + theta) + cos 2 (45 - theta) / tan (60 + theta) tan (30 - theta) = 1