Question

Prove that
tan theta - sin theta / tan theta + sin theta = sec theta - 1 / sec theta + 1
(Using LHS/RHS method)



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Answer 1

Step-by-step explanation:

Given :-

(Tan θ - Sin θ)/(Tan θ + Sin θ)

To find :-

(Tan θ - Sin θ)/(Tan θ + Sin θ) = (Sec θ-1)/(Sec θ+1)

Solution :-

On taking LHS

(Tan θ - Sin θ)/(Tan θ + Sin θ)

We know that

Tan θ = Sin θ/ Cos θ

=> [ (Sin θ/Cos θ) - Sin θ] /[ (Sin θ/Cos θ)+ Sin θ]

=> [Sin θ(1/Cos θ)-1]/[Sin θ (1/Cos θ)+ 1]

On cancelling Sin θ in both the numerator and the denominator

=> [(1/Cos θ)-1] /[ (1/Cos θ)+1]

We know that

1/ Cos θ = Sec θ

=> (Sec θ-1)/(Sec θ+1)

=> RHS

=> LHS = RHS

Hence ,Proved.

Answer :-

(Tan θ - Sin θ)/(Tan θ + Sin θ) = (Sec θ-1)/(Sec θ+1)

Used formulae:-

→ Tan θ = Sin θ/ Cos θ

→ 1/ Cos θ = Sec θ

Answer 2

Answer:

Refers to the above attachment

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