Question

If cos θ=0.6 show that (5sin θ -3tan θ) = 0

Answer 1

cos θ = 0.6

cos θ = 6 / 10

cos θ = 3 / 5

As we know that

cos θ = Base / Hypotenuse = B / H

•°•

B / H = 3 / 5

Let B = 3x and H = 5x

Applying Pythagoras Theorem

( Hypotenuse )² = ( Base )² + ( Perpendicular )²

( H )² = ( B )² + ( P )²

( 5x )² = ( 3x )² + ( P )²

25x² = 9x² + P²

P² = 25x² - 9x²

P² = 16x²

( P )² = ( 4x )²

P = 4x

Now,

sin θ = Perpendicular / Hypotenuse

= P / H

= 4x / 5x

= 4 / 5

tan θ = Perpendicular / Base

= P / B

= 4x / 3x

= 4 / 3

Now,

5 sin θ - 3 tan θ

= 5 ( 4 / 5 ) - 3 ( 4 / 3 )

= 4 - 4

= 0

Hence proved.