Question

express all trigonometric ratios in terms of sec theta.

pls frnds

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept

The ratios of the lengths of a triangle's sides are known as trigonometric ratios. These trigonometric ratios link the ratio of a right triangle's sides to the corresponding angle. Sin, cos, and tan, or sine, cosine, and tangent ratios, are the fundamental trigonometric ratios. With the help of sin, cos, and tan, you can calculate the other crucial trig ratios, cosec, sec, and cot.

Given

trigonometric ratios : cosθ, tanθ, cotθ, cosecθ and sinθ

Find

we are asked to express all the trigonometric ratios in terms of secθ

Solution

1) cosθ = 1/secθ

2) tanθ

given identity is, sec²θ= 1 ₊ tan²θ

sec²θ ₋ 1 = tan²θ

∴ tanθ = √sec²θ ₋ 1

3) cotθ

cotθ = 1/tanθ

cotθ = 1/√sec²θ ₋ 1

4) cosecθ

cosecθ can also be written as √cosec²θ

= √1₊cot²θ

= √1₊1/tan²θ

= √1₊tan²θ/tan²θ

= √sec²θ/tanθ

= secθ/√sec²θ₋1

5) sinθ = 1/cosecθ

= 1/secθ/√sec²θ₋1

= √sec²θ₋1/secθ

hence we prove the trigonometric ratios in terms of secθ.

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