verify each identity A 1sint 11sint 1 2 tant sect B tan c

verify each identity

A) 1/sin(t) 1+1/sin(t) + 1 = 2 tan(t) sec(t)

B) (tan() + cot())^2 = sec^2 () + csc^2()

Solution

A) 1/sin(t) 1+1/sin(t) + 1 = 2 tan(t) sec(t)

LHS : 1/(sint -1) + 1/(1+sint)

(sint +1 + (sint -1))t)/(1- sin^2t)

2sint/cos^2t

2tant/cost = 2tant*sect

RHS

B) (tan() + cot())^2 = sec^2 () + csc^2()

LHS (tan() + cot())^2 = tan^2 + cot^2 +2tancot

= tan^2 + cot^2 +2

= tan^2 +1 +cot^2 +1

= sec^2 + csc^2

=RHS