Question

If cotθ=4, find the value of 5 sin θ−3 cos θ 5 sin θ+3 cos θ

Answer 1

let the angle theta=A
because I have no symbol of theta

cotA= Base/perpendicular
cotA= 4/1

by Pythagoreans theorem,

(H)^2=(B)^2 + (P)^2

H=(4)^2+(1)^2 under square root

H=2

sinA= perpendicular/hypotenuse
sin A= 1/2

cos A=Base/hypotenuse

cos A=4/2=2

ATQ

(5 Sin A - 3 cos A)(5sin A + 3 cos A)
=( 5×1/2 - 3 ×2) ( 5×1/2 + 3×2)
=(5-12/2)(5/2+6)
=(5-12/2)(5+12/2)
=( -7/2) (17/2)
=( -119/4)

Hope u got it!