Question

Verify root 1 -cos theta/1+cos theta =sin theta /1+costheta for theta=60

Answer 1

Question :- verify √{(1 - cosA) / (1 + cosA)} = sinA/(1 + cosA) for A = 60° ?

Solution :-

Putting A = 60° in LHS we get,

→ √{(1 - cos60°) / (1 + cos60°)}

Now, Putting value of cos60° = (1/2) ,

→ √{(1 - 1/2) / (1 + 1/2)}

→ √{(1/2) / (3/2)}

→ √{ (1/2) * (2/3)}

→ √(1/3)

→ (1/√3)

Rationalize the denominator now,

→ (1/√3) * (√3/√3)

→ (√3) / (√3)²

→ (√3/3)

Putting A = 60° in RHS now,

→ sin60° / (1 + cos60°)

Now, putting value of sin60° = (√3/2) and cosA = (1/2)

→ (√3/2) / (1 + 1/2)

→ (√3/2) / (3/2)

→ (√3/2) * (2/3)

→ (√3/3) .

we get,

→ LHS = RHS . (Hence, Verified.)

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Answer 2

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