Question

Prove that ✓(1-sin a/1+sin a)=sec a-tan a

Answer 1

so:-
√1-sina/1+sina
√(1-sina)(1+sina)x√(1-sina)/(1-sina)
√(1-sina)²/(1-sin²a)
√(1-sina)²/cos²a
(1-sina)/cos
(1-cosa-sina/cosa)
seca-tena.

Answer 2

√{(1 - sina)/(1 + sina)} = seca - tana

Step-by-step explanation:

L.H.S. = √{(1 - sina)/(1 + sina)}

= √[{(1 - sina)(1 - sina)}/{(1 + sina)(1 - sina)}]

= √{(1 - sina)²/(1 - sin²a)}

= √{(1 - sina)²/cos²a}

= √{(1 - sina)/cosa}²

= (1 - sina)/cosa

= 1/cosa - sina/cosa

= seca - tana = R.H.S.

Hence proved.

Trigonometry: Trigonometry is the study of angles and relations between angles and their sin, cos, tan, cosec, sec, cot ratios. There are many formulae for calculations:

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin2A = 2 sinA cosA

• cos2A = cos²A - sin²A

• tan2A = 2 tanA / (1 - tan²A)