Question

Prove if the following Trigonometric Identities are true (with solution);

1. csc A tan A = sec A
2. sin A/csc A + cos A/sec A = 1

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• cscA = $\frac{1}{sinA}$

• secA = $\frac{1}{cosA}$

• tanA = $\frac{sinA}{cosA}$

• sin²A + cos²A = 1

(1)

consider the left side

cscA tanA

= $\frac{1}{sinA}$ × $\frac{sinA}{cosA}$ ( cancel sinA )

= $\frac{1}{cosA}$

= secA

= right side ⇒ proven

(2)

consider the left side

$\frac{sinA}{cscA}$ + $\frac{cosA}{secA}$

= $\frac{sinA}{\frac{1}{sinA} }$ + $\frac{cosA}{\frac{1}{cosA} }$

= sinA × sinA + cosA × cosA

= sin²A + cos²A

= 1

= right side ⇒ proven