Question

If sinA=1/2 show that 3cosA -4cos^3A=0

Answer 1

Answer:

Step-by-step explanation:

In a right angled ∆ it is given that

Sin A = 1/2=opp.side/ hypotenuse

Adjacent side =

√[(hypotenuse) ^2-(opp.side) ^2]

= √(4-1) =√3.

Cos A = aaj. Side/hypotenuse= √3 /2

Then,

LHS= 3 cosA-4cos^3A= 3√3/2 -4 (√3/2)^3

= 3√3/2 - 4(3√3/8) = 3√3/2-3√3/2

= 0=RHS

Hence proved.

Answer 2

Step-by-step explanation:

sinA=1÷2

sinA=sin30

eliminate sin on both sides

1.A=30

3cosA-4cos^3A

3cos30degrees-4cos^3 30degrees

3(root3÷2)-4(root3÷2)^3

3root3÷2-4(3)÷8×root3

12root3-12root3÷8

0÷8

0

hence proved