Trigonomtery Class 10 (Question Bank)

 📝 Trigonometry 

Multiple Choice Questions

1. The value of (sin30° + cos30°) – (sin60° + cos60°) is

(A) – 1 

(B) 0 

(C) 1 

(D) 2

Ans: (B)

2. The value of `frac{tan 30°}{cot 60°}` is

(A) `1/sqrt2`

(B) `1/sqrt3`

(C) `sqrt3` 

(D) `1`

Ans: (D)

3. The value of (sin 45° + cos 45°) is

(A) `1/sqrt2`

(B) `sqrt2` 

(C) `sqrt3/2`

(D) 1

Ans: (B)

4. If `cos A = 4/5`,  then the value of `tan A` is

(A) `3/5`

(B) `3/4`

(C) `4/3`

(D) `5/3`

Ans: (B)

5. If `sin A = 1/2`, then the value of `cot A` is

(A) `sqrt3`

 (B) `1sqrt3`

(C) `sqrt3/2`

(D) `1`

Ans: (A)

6. The value of the expression `[cosec (75° + theta) – sec (15° – theta) – tan (55° + theta) + cot (35° – theta)]` is

(A) – 1 

(B) 0 

(C) 1 

(D) `3/2`

Ans: (B)

7. Given that `sin theta = a/b`, then `cos theta` is equal to 

(A) `frac {b}{sqrt (b^2 - a^2)}`

(B) `b/a`

(C) `frac {sqrt (b^2 - a^2)}{b}`

(D) `frac{a}{sqrt (b^2 - a^2)}`

Ans: (C)

8. If `cos (alpha + beta) = 0`, then  `sin (alpha - beta)` can be reduced to 

(A) `cos beta`

(B) `cos2beta`

(C) `sinalpha`

(D) `sin2alpha`

Ans: (B)

9. The value of (tan1° tan2° tan3° ... tan89°) is

(A) 0 

(B) 1 

(C) 2 

(D) `1/2`

Ans: (B)

10. If  `cos9alpha = sinalpha` and `9alpha < 90°`, then value of `tan5alpha`

(A) `1/sqrt3`

(B) `sqrt3` 

(C) 1 

(D) 0

Ans: (C)

11. If `triangleABC` is right angled at C, then the value of `cos (A+B)` is

(A) `0`

(B) `1` 

(C)`1/2`

(D) `sqrt3/2`

Ans: (A)

12. ABC is an isosceles right triangle, right-angled at B. What is the value of `2 \sin A × \cos A`? 

(A) `1/2`  

(B) 1

(C) `3/2`

(D) 2

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Trigonometric Ratios 

1. If cosec `θ` = 2, Show that `(cot θ + \frac{sin  θ}{ 1+ cos  θ}) = 2`

2. If sin  `θ` = `\frac{a^2 - b^2}{ a^2 + b^2}`, find the value of all T-ratios of  `θ`

3. If sin `θ` = `\frac{a}{b}`, show that `(sec θ + tan θ) = \sqrt{\frac{b + a }{b - a}}` 

4. In `\triangle ABC`, `\angleB` = 90°,  `AB = 5 cm` and `(BC + AC) = 25 cm`, find the values of sin A,  cos A, cosec C, sec C.

5. If 7 `sin^2 θ + 3 cos^2 θ = 4`, show that `tan  θ` = `\frac{1}{\sqrt3}`

6. sin `θ` = < 1 (T/F) , cos `θ` = ＜ 1 (T/F). 

7.  In a `\triangle PQR , \angleP = \theta^\circ and \angle R = \varphi^\circ`, `PR =  (x+2) and QR = x`

Find (i)   `(\sqrt {x+1}) cot ɸ`      

        (ii)   `(\sqrt {x^3+ x^2}) tan  θ`

        (iii)  ` cos  θ`

  

8.  If `x = cot A + cos A and y = cot A - cos A`, prove that 

      `\left(\frac{x-y}{x+y}\right)^2 + \left(\frac{x-y}{2}\right)^2 = 1`

9. If `sec \theta + tan \theta = sqrt7`, then find the value of  `(sec \theta - tan \theta)`    (CBSE 2017)

10. If `sin \theta - cos \theta = 0`, then find the value of `(sin^4 \theta + cos^4 \theta)`   (CBSE 2017)

11. If `sin x + cos y = 1, x = 30^\circ` and  `y` is an acute angle then find the value of `y`   (CBSE 2018)

12. If `sec \theta = ( x + \frac{1}{4x}), x \ne 0`, find the value of `(sec \theta + tan \theta)`    (CBSE 2019)

Particular Angles

1.  `\frac {cos 45°}{sec 30° + cosec  30°}`   (NCERT)

2.    `\frac {sin 30^\circ}{cos 45^\circ} +   \frac {cot 45^\circ}{sec 60^\circ} - \frac {sin 60^\circ}{tan 45^\circ} + \frac {cos30^\circ}{sin 90^\circ}`

Work in progress..