Prove that:
(i) sin 60° cos 30° + cos 60° . sin 30° = 1
(ii) cos 30° . cos 60° -sin 30° . sin 60° = 0
(iii) cosec2 45° -cot2 45° = 1
(iv) cos2 30° -sin2 30° = cos 60° .
(v)
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios:
(i) sin 45°
(ii) cos 45°
(iii) tan 45°
(i) If sin x = cos x and x is acute, state the value of x.
(ii) If sec A = cosec A and 0° A 90° , state the value of A.
(iii) If tanθ = cotθ and 0° <= θ <= 90° , state the value of θ.
(iv) If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
(i) If sin x = cos y, then x + y = 45° ; write true of false.
(ii) secθ . Cotθ = cosecθ ; write true or false.
(iii) For any angle, state the value of : Sin2θ + cos2θ .
Given A = 60° and B = 30° , prove that:
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) cos (A + B) = cos A cos B - sin A sin B
(iii) cos (A - B) = cos A cos B + sin A sin B
(iv) tan (A - B) =
If A =30° , then prove that:
(i) sin 2A = 2sin A cos A = 𝟐𝒕𝒂𝒏𝑨/ 𝟏+𝒕𝒂𝒏𝟐𝑨
(ii) cos 2A = cos2A - sin2A= 𝟏−𝒕𝒂𝒏𝟐𝑨/ 𝟏+𝒕𝒂𝒏𝟐𝑨
(iii) 2 cos2 A - 1 = 1 - 2 sin2A
(iv) sin 3A = 3 sin A - 4 sin3A
If A = B = 45° , show that:
(i) sin (A - B) = sin A cos B - cos A sin B
(ii) cos (A + B) = cos A cos B - sin A sin B
If A = 30° ; show that:
(i) sin 3 A = 4 sin A sin (60° -A) sin (60° + A)
(ii) (sin A - cos A)2 = 1 - sin 2A
(iii) cos 2A = cos4 A - sin4 A
(iv) 𝟏−𝒄𝒐𝒔 𝟐𝑨/ 𝒔𝒊𝒏 𝟐𝑨 = 𝒕𝒂𝒏𝑨
(v) 𝟏+𝒔𝒊𝒏𝟐𝑨+𝒄𝒐𝒔𝟐𝑨/ 𝒔𝒊𝒏𝑨+𝒄𝒐𝒔 𝑨 = 𝟐𝒄𝒐𝒔 𝑨
(vi) 4 cos A cos (60° -A). cos (60° + A) = cos 3A
(vii) 𝑐𝑜𝑠3𝐴−𝑐𝑜𝑠3𝐴/ 𝑐𝑜𝑠𝐴
If 4 sin2 𝜽 - 1= 0 and angle 𝜽 is less than 90° , find the value of 𝜽 and hence the value of cos2 𝜽 + tan2 𝜽.
(i) If sin x + cos y = 1 and x = 30° , find the value of y.
(ii) If 3 tan A - 5 cos B= √𝟑 and B = 90° , find the value of A.
From the given figure, find:
(i) cos x °
(ii) x °
(iii) 𝟏 𝒕𝒂𝒏𝟐𝒙° − 𝟏 𝒔𝒊𝒏𝟐𝒙°
(iv) Use tan xo , to find the value of y.
Use the given figure to find:
(i) tan 𝜽°
(ii) 𝜽°
(iii) sin2 𝜽 °
-cos2 𝜽°
(iv) Use sin 𝜽 ° to find the value of x.
Solve for x:
(i) 2 cos 3x - 1 = 0
(ii) Cos 𝒙/ 𝟑 − 𝟏 = 0
(iii) sin (x + 10o ) = ½
(iv) cos (2x - 30° ) = 0
(v) 2 cos (3x - 15° ) = 1
(vi) tan2 (x - 5 ° ) = 3
(vii) 3 tan2 (2x - 20° ) = 1
(viii) Cos ( 𝒙/ 𝟐 +𝟏𝟎) = √𝟑/ 𝟐
(ix) sin2 x + sin2 30° = 1
(x) cos2 30° + cos2 x = 1
(xi) cos2 30° + sin2 2x = 1
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