Question

show that 1/ cos theta - cos theta= tan theta - sin theta
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Answer 1

Answer:

Above is the Answer for your solution

Step-by-step explanation:

l hope you have understood

Answer 2

Correct Question:

1 / cos θ - cos θ = tan θ . sin θ

Answer:

1 / cos θ - cos θ = tan θ . sin θ

Step-by-step-explanation:

We have to show that, 1 / cos θ - cos θ = tan θ . sin θ.

We can prove this equation by considering LHS of the equation.

LHS = 1 / cos θ - cos θ

LHS = ( 1 - cos² θ ) / cos θ

LHS = sin² θ / cos θ - - [ ∵ sin² θ + cos² θ = 1 ]

LHS = sin θ × sin θ / cos θ

LHS = sin θ / cos θ × sin θ

LHS = tan θ . sin θ - - [ ∵ tan θ = sin θ / cos θ ]

∴ LHS = RHS

Hence shown!

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We can prove the given equation by considering RHS of the equation.

RHS = tan θ . sin θ

RHS = sin θ / cos θ × sin θ - - [ ∵ tan θ = sin θ / cos θ ]

RHS = sin θ × sin θ / cos θ

RHS = sin² θ / cos θ

RHS = ( 1 - cos² θ ) / cos θ - - [ ∵ sin² θ + cos² θ = 1 ]

RHS = 1 / cos θ - cos² θ / cos θ - - [ Separating the denominator ]

RHS = 1 / cos θ - cos θ

∴ RHS = LHS

Hence shown!

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Additional Information:

Basic Trigonometric Identities:

1. tan θ = sin θ / cos θ

2. sin² θ + cos² θ = 1

3. 1 + tan² θ = sec² θ

4. 1 + cot² θ = cosec² θ