3rd Year HS : Trigometric Identities.

Hello guys.

I'm really having difficulties in answering Trigometric identities

kindly help me with this.


This is the Fundamental Trigonometric Identities Chart that my teacher gave me.



and this the problem that I need to prove.

Prove.


please explain them to me .

and can I ask for techniques or ways to answer this without difficulties?

[MAS1]

1. 1 - sin/csc = cos/sec

Let's work on the left-hand side (LHS).

1 - sin/(1/sin) = cos/sec

1 - sin*sin = cos/sec

cos*cos = cos/sec

cos(1/sec) = cos/sec

cos/sec = cos/sec


2. 1/(sec*sec) = 1 - 1/(csc*csc)

Work on the RHS.

1/(sec*sec) = 1 - 1/((1/sin)(1/sin))

1/(sec*sec) = 1 - sin*sin

1/(sec*sec) = cos*cos

1/(sec*sec) = (1/sec)(1/sec)

1/(sec*sec) = 1/(sec*sec)