Question

If sin A=0.8 then prove that 5cos A+3tan A=7

Answer 1

Answer:

In the above ∆ABC

Angle A = β

Given that,

sinA = 0.8

sinβ = 0.8

sinβ = 8/10 = opposite/Hypotenuse

Now,

By comparing

Opposite = 8 cm

Hypotenuse = 10 cm

Finding the third side by Pythagoras theorem

(hypotenuse)² = (side)² + +side)²

AC² = AB² + BC²

10² = AB² + 8²

100 = AB² + 64

100 - 64 = AB²

AB² = 36

AB = √36

AB = 6 cm

To find:

Prove that 5cosA + 3tanA = 7

Taking LHS

We know that cosA = adjacent/hypotenuse

tanA = opposite/hypotenuse

= 5cosβ + 3tanβ

= 5×6/10 + 3×8/6

= 3 + 4

= 7

LHS = RHS

Hence proved