Question

evaluate:4-tansquareteta+secsquareteta​

Answer 1

Answer- The above question is from the chapter 'Trigonometric Identities'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Trigonometric Identites:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Question: Evaluate- 4 - tan²θ + sec²θ

Solution:

By arrangement in the form of identlity,

4 - tan²θ + sec²θ

= 4 + sec²θ - tan²θ

     We know that sec²θ - tan²θ = 1

= 4 + 1

= 5

∴ 4 - tan²θ + sec²θ = 5                        

Answer 2

♦To Find♦

Value of : 4–tan²θ+sec²θ

★★Solution★★

OR 4+(sec²θ−tan²θ)

As, sec²θ=1+tan²θ

» 4+(1)

» 5

♠Answer♠

∴ 5 is the value of the given expression.