Advertisements
Advertisements
Question
If θ = 30°, verify that: 1 - sin 2θ = (sinθ - cosθ)2
Advertisements
Solution
Given: θ = 30°
1 - sin2θ
= 1 - sin2 x 30°
= 1 - sin60°
= `1 - sqrt(3)/(2)`
= `(2 - sqrt(3))/(2)`
(sinθ - cosθ)2
= sin2θ + cos2θ - 2sinθ cosθ
= 1 - 2 x sin30° x cos30
= `1 - 2 xx (1)/(2) xx sqrt(3)/(2)`
= `1 - sqrt(3)/(2)`
= `(2 - sqrt(3))/(2)`
⇒ 1 - sin2θ = (sinθ - cosθ)2.
APPEARS IN
RELATED QUESTIONS
Solve the following equation for A, if 2 sin 3 A = 1
Solve for x : cos (2x - 30°) = 0
Solve for 'θ': cot2(θ - 5)° = 3
If θ = 30°, verify that: sin 3θ = 4sinθ . sin(60° - θ) sin(60° + θ)
Evaluate the following: `((sin3θ - 2sin4θ))/((cos3θ - 2cos4θ))` when 2θ = 30°
If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.
Find the value of 'y' if `sqrt(3)` = 1.723.
Given your answer correct to 2 decimal places.
If tan x° = `(5)/(12) . tan y° = (3)/(4)` and AB = 48m; find the length CD.
Evaluate the following: `(tan12°)/(cot78°)`
Evaluate the following: sin22° cos44° - sin46° cos68°
