Question

Evaluate the following:
(1) sec 12º.cosec 78° - tan 12º.cot 78°​

Answer 1

Answer:

1

Step-by-step explanation:

We know that

cosec(90˚-θ)=secθ        and            cot(90˚-θ)=tanθ

Then,

sec12˚cosec78˚ - tan12˚cot78˚

=sec12˚cosec(90˚-12˚) - tan12˚cot(90˚-12˚)

=sec12˚sec12˚ - tan12˚tan12˚

=sec²12-tan²12

=1                                                     [sec²θ-tanθ²=1]