Question

Sec square theta minus tan square theta is equal to

Answer 1

Answer:

Step-by-step explanation:

it is equal to 1 Since see attachment

Answer 2

Given: sec²θ-tan²θ

To find The value of sec²θ-tan²θ

Solution: While we study mathematics, there is a branch which is called trigonometry. The ratios of trigonometry are divided into three basic types and they are sin, cos, and tan. There are also the reciprocals of sin, cos, tan while we will solve problems of trigonometric ratios and they are cosec, sec, cot respectively.

Now if we consider an angle θ, then sin θ=1/cosec θ, cos θ=1/sec θ, tan θ=1/cot θ and vice-versa.

We know that sin²θ+cos²θ=1 and tan θ=sin θ/cos θ

⇒ cos²θ=1-sin²θ / sin²θ=1-cos²θ

∴ sec²θ-tan²θ

= (1/cos²θ)-(sin²θ/cos²θ)  [∵ tan θ=sin θ/cos θ and sec θ=1/cos θ]

=(1-sin²θ)/cos²θ  [∵ The denominator of the two terms are same then the terms on the numerator are added]

= cos²θ/cos²θ [ ∵cos²θ=1-sin²θ]]

= 1   [The numerator and the denominator terms are the same so its division comes as 1]

Hence the value of  sec²θ-tan²θ is 1.