# Trigonometry - Aptitude Questions and Answers

 If 7sin2 x +3cos2 x = 4, 0 < x < 90º ,then what is the value of tan x? A) √2 B) 1 C) √3/2 D) 1/√3 Correct Answer : 1/√3 Explanation :7sin2 x +3cos2 x = 4 7sin2 x/cos2 x + 3cos2 x/cos2 x = 4/cos2 x 7tan2 x + 3 = 4sec2 x ​​​​​​​7tan2 x + 3 = 4(1+tan2 x) ​​​​​​​​​​​​​​3tan2 x = 1 ​​​​​​​​​​​​​​tan x = 1/√3 Post/View Answer Post comment Cancel Thanks for your comment.! Write a comment(Click here) ...
 What is the value of cot 4π/3 ? A) 1/√3 B) -√3 C) -1 D) √3 Correct Answer : 1/√3 Explanation :cot 4π/3 = cos 4π/3 / sin 4π/3 = -1/2 / -√3/2 = 1/√3 What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ? A) √2 B) 2√2 C) √2 tanx D) 0 Correct Answer : √2 Explanation :sinx √( 1 /1+cosx + 1 /1-cosx ) =sinx √( 1-cosx + 1+cosx / (1+cosx ) (1-cosx) ) =sinx √( 2 / (1 - cos2x ) ) =sinx √ (2 / sin2x) =sinx √ 2 / sinx =√ 2 What is cos4 A - sin4 A / cos2 A - sin2 A equal to? A) cos2 A - sin2 A B) cos A - sin A C) 1 D) 2 Correct Answer : 1 Explanation :cos4 A - sin4 A / cos2 A - sin2 A = (cos2 A)2 - (sin2 A)2 / cos2 A - sin2 A = (cos2 A + sin2 A) (cos2 A - sin2 A) / (cos2 A - sin2 A) = (cos2 A + sin2 A) (cos2 A - sin2 A) / (cos2 A - sin2 A) = (cos2 A + sin2 A) ​​​​​​​​​​​​​​= 1 If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x2 + y2 equal to? A) 2ab B) a + b C) a2 + b2 D) a2 - b2 Correct Answer : a2 + b2 Explanation :x2 + y2 = (a cosθ + b sinθ)2 + (a sinθ - b cosθ)2 = (a2 cos2θ + b2 sin2θ + 2*ab* cosθ*sinθ) + (a2 cos2θ + b2 sin2θ - 2*ab* cosθ*sinθ) = (a2 cos2θ + b2 sin2θ + a2 cos2θ + b2 sin2θ ) = a2(cos2θ + sin2θ) + b2 (cos2θ + sin2θ)​​​​​​​ = a2+ b2 2 tan 45° /( 1+ tan2 45°) = ? A) sin 90° B) tan 30° C) tan 90° D) sin 45° Correct Answer : sin 90° Explanation :2 tan 45° /( 1+ tan2 45°) = 2 / (1 + 12) (tan 45°=1) = 1 = sin 90° If sinA= 8/17 and cosA=15/17, then cotA=? A) 17/8 B) 8/15 C) 17/15 D) 15/8 Correct Answer : 15/8 Explanation :As given sinA = 8/17 = perpendicular/hypotenuse cosA= 15/17 = base/hypotenuse tanA = sinA/cosA = perpendicular/base = 8/15 cotA = 1/tanA = base/perpendicular = 15/8
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