Question

Prove that
2 (Cos⁴ 60°+sin⁴30°)-(tan²60° + cot²45°)+3sec²30°= 1/4​

Answer 1

Answer:

L.H.S:

[2(cos⁴ 60°+sin⁴30°)]-(tan²60° + cot²45°)+3sec²30°

=[2{(1/2)^4+(1/2)^4}]-{(√3)^2+(1)^2}+3(2/√3)^2

=2(1/16+1/16)-(3+1)+3×4/3

=(2×1/8)-4+4

=1/4=R.H.S

Hence, proved.