Question

1. (Cosec A+1)/(cosec A-1) =(1+sin A)/(1-sin A)

2. (sec A -1 )/(Sec A +1)= (1-cos A)/(1+cos a)

(Brackets r just to separate the identities

Answer 1

Answer:

1. LHS : (cosecA -1)/(cosecA + 1) = [(1/sinA) - 1] / [ (1/sinA) + 1]

= [(1-sinA)/(1 + sinA)]

Multiplying both numerator and denominator with (1 + sinA)

= [(1-sinA)*(1+sinA)] / [(1+sinA)*(1 + sinA)]

= [1-square(sinA)][square(1 +sinA)]

= square(cosA)/square(1 + sinA)

= square[cosA / (1 + sinA)]

= RHS.