Trigonometry

Without using trigonometric tables, prove that:

(sin72° + cos18°)(sin72° − cos18°) = 0

Using trigonometric table evaluate the following:
cos 64°42' - sin 42°20'

Solve the following equation: `(cos^2θ - 3 cosθ + 2)/sin^2θ` = 1.

Prove that `(sin "A" - cos "A" + 1)/(sin "A" + cos "A" - 1) = 1/(sec "A" - tan "A")`

Using trigonometric table evaluate the following:
tan 78°55' - tan 55°18'

Prove that:

\[\frac{\sin\theta}{\cos(90° - \theta)} + \frac{\cos\theta}{\sin(90° - \theta)} = 2\]

In the below given figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20√3 m long. Find the sun’s altitude. 

Without using trigonometric tables, prove that:

sin²48° + sin²42° = 1