Question

if x=sin theta + cos theta y =sin theta×cos theta then eliminate theta​

Answer 1

Topic

Elimination of parameters

Given

x = sinθ + cosθ

y = sinθ × cosθ

Formula to be used

( sinθ + cosθ )² = 1 + 2sinθcosθ

Solving

To eliminate θ, we will first square 'x' and then use value of y.

( sinθ + cosθ )² = 1 + 2sinθcosθ

x² = 1 + 2y

as it is given that

x = sinθ + cosθ

y = sinθ × cosθ

Answer

On eliminating θ, we get

x² = 1 + 2y

Some Trigonometric Formulae

sin 3θ = 3sinθ - 4sin³θ

cos 3θ = 4cos³θ - 3cosθ

sin 2θ = 2sinθ × cosθ