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 sin⁡Θ/(1+cos⁡Θ )= cosecΘ - cotΘ

Solution:

Consider LHS sin⁡Θ/(1+cos⁡Θ )
Multiply and divided by 1-cos⁡Θ
sin⁡Θ/(1+cos⁡Θ ) x 1-cos⁡Θ/1-cosΘ
1- cos⁡Θ(sin⁡Θ)/1^2 - cos^2Θ
(1- cos⁡Θ)(sin⁡Θ)/sin^2 Θ
(1- cos⁡Θ)/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°× csc⁡315°

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)