Question

prove that (1+tan theta + sec theta) (1+cot theta- cosec theta) = 2​

Answer 1

Step-by-step explanation:

TAKING LHS

(1+tan Q + sec Q) (1+ot Q-cosc Q)

( 1+sinQ/cosQ+1/cosQ)(1+cosQ/sinQ-1/sinQ)

[(cosQ+sinQ+1)/cosQ][(sinQ+cosQ-1)/sinQ]

[(cosQ+sinQ+1)][(sinQ+cosQ-1)]/sinQcosQ

using identity

using identity(a + b) (a - b) = a^2- b^2

[(cosQ+sinQ)^2 -1^2]/sinQcosQ

(cos^2+sin^2Q+2cosQsinQ -1)/sinQcosQ

1 -1 + 2sinQcosQ/sinQcosQ

2sinQcosQ/sinQcosQ

= 2. = RHS