# Important Questions for Chapter 3 - Trigonometric function

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**Important questions based on NCERT syllabus Chapter 3-Trignometric function:**

*Question 1*: Prove that sinΘ/(1+cosΘ )= cosecΘ - cotΘ

*Solution*:

Consider LHS sinΘ/(1+cosΘ )

Multiply and divided by 1-cosΘ

sinΘ/(1+cosΘ ) x 1-cosΘ/1-cosΘ

1- cosΘ(sinΘ)/1^2 - cos^2Θ

(1- cosΘ)(sinΘ)/sin^2 Θ

(1- cosΘ)/sinΘ

1/sinΘ - cosΘ/sinΘ

cosecΘ - cotΘ

*Question 2*: Evaluate 2 sin(120°) + 4 cos(120°) give

a) exact answer ,

b) approximate to nearest hundredth.

*Solution*:

sin(120°)= √3/2 ; cos(120°)=-1/2

2 sin(120°) + 4 cos(120°)

= 2(√3/2) + 4(-1/2)

= √3-2

a) Exact value: √3-2

b) Approximate value: -0.27

*Question 3*: Evaluate

sin 300° ×tan 330° ×sec 60°/cot 135°×cos 210°× csc315°

*Solution*:

sin 300° × tan 330° × sec 60°/cot 135° × cos 210° × csc 315°

=((-√3/2) × (-√3/3)×(2))/((-1) × (-√3/2) × (-√2))

=((-√3/2) × (-√3/3) × (2))/((-1) × (-√3/2) × (-√2))

=1/((-√3/√2) )

=-√(2/3)