SSC CGL Previous Year Questions: Trigonometry - 5 - SSC CGL

In a triangle ABC, AB = AC, BA is produced to D in such a manner that AC = AD. The circular measure of ∠BCD is    (SSC CGL 2nd Sit. 2012)

The radian measure of 63°14'51" is   (SSC CGL 2nd Sit. 2012)

If sec θ + tan θ = √3, then the positive value of sin θ is    (SSC CGL 2nd Sit. 2012)

If 2y cos θ = x sin θ and 2x sec θ – y cosec θ = 3, then the relation between x and y is    (SSC CGL 2nd Sit. 2012)

If sinθ + sin²θ = 1, then the value of cos¹²θ + 3cos¹⁰θ + 3cos⁸θ + cos⁶θ – 1 is    (SSC CGL 1st  Sit. 2012)

When the angle of elevation of the sum increases from 30° to 60°, the shadow of a post is diminished by 5 metres. then the height of the post is    (SSC CGL 1st  Sit. 2012)

If 0 ≤ 2 ≤ π/2, 2y cosθ = x sin θ and 2x secθ – y cosecθ = 3, then the value of x² + 4y² is    (SSC CGL 1st  Sit. 2012)

If x = cosecθ – sinθ and y = secθ – cosθ, then the value of x²y² (x² + y² + 3) is     (SSC CGL 1st  Sit. 2012)

If tan (x + y) tan (x – y) = 1, then the value of tan (2x/3) is   (SSC CGL 1st  Sit. 2012)

The least value of (4sec²θ + 9 cosec²θ) is    (SSC CGL 1st  Sit. 2012)

If 5 tanθ = 4, then the value of     (SSC CGL 1st  Sit. 2012)

If x, y are positive acute angles, x + y < 90° and sin (2x – 20°) = cos (2y + 20°), then the value of sec (x + y) is    (SSC CGL 2nd  Sit. 2012)

If α is a positive acute angle and 2sinα + 15cos²α = 7, then the value of cotα is:   (SSC CGL 2nd  Sit. 2012)

If (a² – b²) sinθ + 2ab cosθ = a² + b², then the value of tanθ is    (SSC CGL 2nd  Sit. 2012)

If tan θ – cot θ = a and cos θ – sin θ = b, then the value of (a² + 4) (b² – 1)² is:   (SSC CGL 2nd  Sit. 2012)

If a³ – b³ = 56 and a – b = 2, then the value of (a² + b²) is:    (SSC CGL 2nd  Sit. 2012)

The simplified value of    (SSC CGL 2nd  Sit. 2012)

The least value of 4 cosec²α + 9sin²α is:   (SSC CGL 2nd  Sit. 2012)

If tan(x + y) tan (x – y) = 1, then the value of tan x is:    (SSC CGL 2nd Sit. 2012)

A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of 50√3 m, then its speed in km/h is:    (SSC CGL 2nd Sit. 2012)

In a right-angled triangle ABC, ÐB is the right angle and AC = 2√5 cm. If AB – BC = 2 cm, then the value of (cos²A – cos²C) is:   (SSC CGL 2nd Sit.  2012)

If cot A + cosec A = 3 and A is an acute angle, then the value of cos A is:    (SSC CGL 2nd Sit. 2012)

If cos A + cos² A = 1, then sin² A + sin⁴ A is equal to   (SSC CGL 1st Sit. 2012)

A tree is broken by the wind. If the top of the tree struck the ground at an angle of 30° and at a distance of 30 m from the root, then the height of the tree is    (SSC CGL 1st Sit.2012)

sec⁴θ – sec²θ is equal to   (SSC CGL 1st Sit. 2012)

If x sin³ θ + y cos³ θ = sin θ cos θ and x sin θ = y cos θ, sin θ ≠ 0, cos θ ≠ 0, then x² + y² is        (SSC CGL 1st Sit. 2012)

If sin θ + cos θ = √2 cos (90° – θ), then cot θ is    (SSC CGL 1st Sit. 2012)

If 2 – cos 2θ = 3 sin θ cos θ, sin θ ≠ cos θ then tan θ is   (SSC CGL 1st Sit. 2012)

    (SSC CGL 1st Sit. 2012)

The least value of 2 sin² θ + 3 cos² θ is    (SSC CGL 1st Sit. 2012)

If A and B are complementary angles, then the value of sin A cos B + cos A sin B – tan A tan B + sec² A – cot² B is    (SSC CGL 1st Sit. 2012)

P and Q are two points observed from the top of a building 10√3 m high. If the angles of depression of the points are complementary and PQ = 20 m, then the distance of P from the building is   (SSC CGL 1st Sit. 2012)

 value of cos θ is:    (SSC CHSL 2012)

 then value of cot θ is:   (SSC CHSL 2012)

 then the value of sin 2θ₁ + tan 3θ₂ is equal to (Assume that 0 < θ₁ - θ₂ < θ₁ + θ₂ < 90°)    (SSC Sub. Ins. 2012)

The value of (sec θ – cos θ) (cosec θ – sin θ) (tan θ + cot θ) is   (SSC Sub. Ins. 2012)

tan 7° tan 23° tan 60° tan 67° tan 83° is equal to   (SSC Sub. Ins. 2012)

A ladder is resting against a wall at height of 10m. If the ladder is inclined with the ground at an angle of 30°, then the distance of the foot of the ladder from the wall is    (SSC Sub. Ins. 2012)