Selina solutions concise maths class 9 icse Solutions for Chapter 23 chapter 23 trigonometrical ratios of standard angles

(i) sin 30° cos 30°

(ii) tan 30° tan 60°

(iii) cos2 60° + sin2 30°

(iv) cosec2 60° -tan2 30°

(v) sin2 30° + cos2 30° + cot2 45°

(vi) cos2 60° + sec2 30° + tan2 45° .

(i) tan2 30° + tan2 45° + tan2 60°

(ii)

(iii) 3 sin2 30° + 2 tan2 60° -5 cos2 45° .

(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)

(vi) 3 cosec2 60° -2 cot2 30° + sec2 45° = 0.

(i) sin 45°

(ii) cos 45°

(iii) tan 45°

(i) sin 60° = 2 sin 30° cos 30° .

(ii) 4 (sin4 30° + cos4 60° )-3 (cos2 45° -sin2 90° ) = 2

(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 .

(i) sin 60°

(ii) 2/tan 30°

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 = ?????/ ?+?????

(ii) cos 2A = cos2A – sin2A= ?−?????/ ?+?????

(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) ?−??? ??/ ??? ?? = ????

(v) ?+?????+?????/ ????+??? ? = ???? ?

(vi) 4 cos A cos (60° -A). cos (60° + A) = cos 3A

(vii) ???3?−???3?/ ????

• ???3?−???3?/ ???? = 3

If 2 sin x° -1 = 0 and xo is an acute angle; find :

(i) sin x °

(ii) x °

(iii) cos x ° and tan xo .

If 4 sin2 ? – 1= 0 and angle ? is less than 90° , find the value of ? and hence the value of cos2 ? + tan2 ?.

If sin 3A = 1 and 0 <= A <= 90° , find:

(i) sin A

(ii) cos 2A

(iii) ???2? − 1/ ???2A

(iii) sin2 (75° -A) + cos2 (45° +A)

(i) If sin x + cos y = 1 and x = 30° , find the value of y.

(ii) If 3 tan A – 5 cos B= √? and B = 90° , find the value of A.

(i) cos x °

(ii) x °

(iii) ? ?????° − ? ?????°

(iv) Use tan xo , to find the value of y.

(iv) Use sin ? ° to find the value of x.

(iv) cos (2x – 30° ) = 0

(v) 2 cos (3x – 15° ) = 1

(vi) tan2 (x – 5 ° ) = 3

(vii) 3 tan2 (2x – 20° ) = 1

(viii) Cos ( ?/ ? +??) = √?/ ?

(ix) sin2 x + sin2 30° = 1

(x) cos2 30° + cos2 x = 1

(xi) cos2 30° + sin2 2x = 1

(xii) sin2 60° + cos2 (3x- 9 ° ) = 1

In triangle ABC, angle B = 90° , AB = y units, BC = √? units, AC = 2 units and angle A = xo , find:

(i) sin x°

(ii) x °

(iii) tan x°

(iv) use cos x ° to find the value of y.