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Trigonometry Exercise Notes 2021 Download Study Materials BOOK PDF

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  1. sin^2⁡θ+cos^2⁡θ=1
  2. cosec^2⁡θ-cot^2⁡θ=1
  3. sec^2⁡θ=tan^2⁡θ=1
  4. sin⁡(90°-θ)=cos⁡θ
  5. cos⁡(90°-θ)=sin⁡θ
  6. tan⁡(90°-θ)=cot⁡θ⇒ cot⁡〖(90°-θ)=tan⁡θ 〗
  7. cosec⁡(90°-θ)=sec⁡θ
  8. sec⁡(90°-θ)=cosec⁡θ

Example 1: In a ΔABC right angled at B if AB = 12, and BC = 5 find sin A and tan A, cos C and cot C

AC=√((AB)^2+(BC)^2 )
=√(〖12〗^2+5^2 )
When we consider t-ratios of∠A we have
Base AB = 12
Perpendicular = BC = 5
Hypotenuse = AC = 13
When we consider t-ratios of ∠C, we have
Base = BC = 5
Perpendicular = AB = 12
Hypotenuse = AC = 13

Example 2: In a right triangle ABC right angle at B the six trigonometric ratios of C

Base=√((Hypotenuse)^2-(Perpendicualr)^2 )
=√(5^2-3^2 )

Example 3: Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°

Example 4:bFind the value θ sin2θ=√3
sin⁡2θ= √3/2
2θ = 60
θ = 30°

Example 5: Find the value of x. Tan 3x = sin 45° cos 45° + sin 30°
⇒tan⁡3x=1 ⇒tan⁡3x=tan⁡〖45°〗
3x = 45°
X = 15°

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