Trigonometric Functions — Class 11 solved problems

33 problems from this chapter, each solved step by step.

If sin A + sin B + sin C = cos A + cos B + cos C = 0, prove that sin² A + sin² B + sin² C = cos² A + cos² B + cos² C = 3/2.
sin² A + sin² B + sin² C = (3)/(2) and cos² A + cos² B + cos² C = (3)/(2).
Find the value of tan (π)/(8).
√2 - 1
Prove that =(sin 5 x-2 sin 3 x+sin x)/(cos 5 x-cos x)=tan x
The proof is complete, as (sin 5 x-2 sin 3 x+sin x)/(cos 5 x-cos x)=tan x.
The sum of all values of θ [0, 2π] satisfying 2sin² θ = cos 2θ and 2cos² θ = 3sin θ is:
π
Prove that 3 sin (π)/(6) sec (π)/(3)-4 sin (5 π)/(6) cot (π)/(4)=1
The given equation is proven to be true, as the left-hand side simplifies to 1.
If cos x=-(3)/(5), x lies in the third quadrant, find the values of other five trigonometric functions.
The values of the other five trigonometric functions are: sin x = -(4)/(5), tan x = (4)/(3), csc x = -(5)/(4), sec x = -(5)/(3), and cot x = (3)/(4).
Convert 40^(°) 20^() into radian measure.
(121π)/(540) radians
If sin x=(3)/(5), cos y=-(12)/(13), where x and y both lie in second quadrant, find the value of sin (x+y).
-(56)/(65)
If for θ [ -(π)/(3), 0 ], the points (x, y) = ( 3 tan(θ + (π)/(3)), 2 tan(θ + (π)/(6))) lie on xy + α x + β y + = 0, then α² + β² + ² is equal to:
337
In a triangle ABC, if a = 18, b = 24, c = 30 find the value of sin(A/2) and cos(A/2).
sin(A/2) = (√10)/(10) and cos(A/2) = (3√10)/(10).
If sin x + sin² x = 1, x (0, (π)/(2)), then (cos^(12) x + tan^(12) x) + 3(cos^(10) x + tan^(10) x + cos^8 x + tan^8 x) + (cos^6 x + tan^6 x) is equal to:
2
Find the value of x: sin(x) = cos(x) for x in [0, π/2].
x = (π)/(4)
The number of solutions of the equation (4-√3)sin x - 2√3cos²x = -(4)/(1+√3), x [-2π,(5π)/(2)] is equal to:
5
If θ [-2π, 2π], then the number of solutions of 2√2cos²θ + (2-√6)cosθ - √3 = 0 is equal to:
8
Show that tan 3 x tan 2 x tan x=tan 3 x-tan 2 x-tan x
The identity tan 3 x tan 2 x tan x=tan 3 x-tan 2 x-tan x is shown to be true by using the tangent addition formula and algebraic manipulation.
Prove that (cos 7 x+cos 5 x)/(sin 7 x-sin 5 x)=cot x
cot x
If sin A + sin B + sin C = cos A + cos B + cos C = 0 prove that sin²A + sin²B + sin²C = cos²A + cos²B + cos²C = 3/2.
sin²A + sin²B + sin²C = cos²A + cos²B + cos²C = (3)/(2)
If cot x=-(5)/(12), x lies in second quadrant, find the values of other five trigonometric functions.
The values of the other five trigonometric functions are: tan x = -(12)/(5), csc x = (13)/(12), sin x = (12)/(13), cos x = -(5)/(13), and sec x = -(13)/(5).
Let A = x (0, π) - (π)/(2): log_(2 / π) |sin x| + log_(2 / π) |cos x| = 2 and B = x 0: √x (√x - 4) - 3 |√x - 2| + 6 = 0. Then n(A B) is equal to:
8
Find the value of sin (31 π)/(3).
The value of sin (31 π)/(3) is (√3)/(2).
Prove that (sin (x+y))/(sin (x-y))=(tan x+tan y)/(tan x-tan y).
The identity is proven: (sin (x+y))/(sin (x-y))=(tan x+tan y)/(tan x-tan y)
Prove that cos ((π)/(4)+x)+cos ((π)/(4)-x)=√2 cos x
The identity is proven: cos ((π)/(4)+x)+cos ((π)/(4)-x)=√2 cos x.
Find the value of sin 15^(°).
The value of sin 15^(°) is (√6 - √2)/(4).
Let the range of the function f(x) = 6 + 16 cos x · cos ((π)/(3) - x) · cos ((π)/(3) + x) · sin 3x · cos 6x, x R be [α, β]. Then the distance of the point (α, β
11
x का मान ज्ञात कीजिए: sin(x) = cos(x) जहाँ x [0, π/2] के बीच है।
x = (π)/(4)
Find the maximum value of 3cos θ + 4sin θ + 5cos(θ + π/6).
The maximum value of the expression is √(30 + 15√3).
If tan A = 1/7 and tan B = 1/3 find tan(2A + B) without using calculator approximations.
tan(2A + B) = (9)/(13)
Convert 6 radians into degree measure.
343.77^°
If 10sin^4θ + 15cos^4θ = 6 then the value of (27csc^6θ + 8sec^6θ)/(16sec^8θ) is:
(2)/(5)
If θ [-(7π)/(6), (4π)/(3)], then the number of solutions of √3csc²θ - 2(√3 - 1)cscθ - 4 = 0, is equal to:
The number of solutions is 6.
Find the value of tan(π/7)·tan(2π/7)·tan(3π/7).
√7
The number of solutions of the equation cos 2 (θ)/(2) + cos(5θ)/(2) = 2cos³(5θ)/(2) in [-(π)/(2),(π)/(2)] is:
7
Find the value of cos (-1710^(°)).
The value of cos (-1710^(°)) is 0.

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