Question

1+cosa÷sina - sin a ÷1+cos a = 2 cot a
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Answer 1

Topic:

Trigonometry

Question Correction:

1+cosa÷sina + sin a ÷1+cos a = 2cosecA

Answer:

Taking LHS

1+cosA/sinA+SinA/1+CosA

Taking LCM

(1+CosA)²+sin²A/SinA×(1+cosA)

1+cos²A+2cosA+sin²A/sinA×(1+cosA)

Here Cos²A+Sin²A=1

So,

2+2CosA/SinA×(1+CosA)

Take 2 Common

2(1+CosA) /SinA×(1+CosA)

In Numerator and Denominator 1+CosA cancelled

2/SinA= 2×1/sinA

=2 CosecA

Hence Proved ///

More information:

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj