Here we will solve various types of problems on eliminate theta from the given equations.

We know, “eliminate theta from the equations” means that the equations are combined in such a way into one equation that it remains valid without the theta (θ) appearing in this new equation.

Worked-out problems on eliminate theta (θ) between the equations:

x = a sin θ + b cos θ and y = a cos θ – b sin θ

If x = a sin θ + b cos θ and y = a cos θ –b sin θ, prove that

x

We have x

= (a

= a

= a

= a

= a

= a

= a

Therefore, x

which is the required θ-eliminate.

tan θ - cot θ = a and cos θ + sin θ = b.

tan θ – cot θ = a ………. (A)

cos θ + sin θ = b ………. (B)

Squaring both sides of (B) we get,

cos

or, 1 + 2 cos θ sin θ = b

or, 2 cos θ sin θ = b

Again, from (A) we get, (sin θ/cos θ) – (cos θ/sin θ) = a

or, (sin

or, sin

or, (sin θ + cos θ) (sin θ - cos θ) = a ∙ (b

or, b(sin θ - cos θ)= (½) a (b

or, b

or, b

or, b

or, 4b

which is the required θ-eliminate.

Show how to use the trigonometric identities to solve the problems on eliminate theta form the given two equations.

x sin θ - y cos θ = √(x

cos

Squaring both sides of (A) we get,

x

or, x

or, x

or, (x cos θ + y sin θ)

or, x cos θ + y sin θ = 0

or, x cos θ = - y sin θ

or, cos θ/(-y) = sin θ/x

or, cos

Therefore, cos

Putting the values of cos

(1/a

Or, y

which is the required θ-eliminate.

The explanation will help us to understand how the steps are used technically to work-out the problems on eliminate theta form the given equations.

**●** **Trigonometric Functions**

**Basic Trigonometric Ratios and Their Names****Restrictions of Trigonometrical Ratios****Reciprocal Relations of Trigonometric Ratios****Quotient Relations of Trigonometric Ratios****Limit of Trigonometric Ratios****Trigonometrical Identity****Problems on Trigonometric Identities****Elimination of Trigonometric Ratios****Eliminate Theta between the equations****Problems on Eliminate Theta****Trig Ratio Problems****Proving Trigonometric Ratios****Trig Ratios Proving Problems****Verify Trigonometric Identities****Trigonometrical Ratios of 0°****Trigonometrical Ratios of 30°****Trigonometrical Ratios of 45°****Trigonometrical Ratios of 60°****Trigonometrical Ratios of 90°****Trigonometrical Ratios Table****Problems on Trigonometric Ratio of Standard Angle****Trigonometrical Ratios of Complementary Angles****Rules of Trigonometric Signs****Signs of Trigonometrical Ratios****All Sin Tan Cos Rule****Trigonometrical Ratios of (- θ)****Trigonometrical Ratios of (90° + θ)****Trigonometrical Ratios of (90° - θ)****Trigonometrical Ratios of (180° + θ)****Trigonometrical Ratios of (180° - θ)****Trigonometrical Ratios of (270° + θ)****Trigonometrical Ratios of (270° - θ)****Trigonometrical Ratios of (360° + θ)****Trigonometrical Ratios of (360° - θ)****Trigonometrical Ratios of any Angle****Trigonometrical Ratios of some Particular Angles****Trigonometric Ratios of an Angle****Trigonometric Functions of any Angles****Problems on Trigonometric Ratios of an Angle****Problems on Signs of Trigonometrical Ratios**

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