NCERT Exercise 8.2

Question – 1 - Evaluate the following:

(i) sin 60o cos 30o + sin 30o cos 60o





(ii) 2 tan2 45o + cos2 30o - sin2 60o





(iii) `(cos 45°)/(sec 30°+text(cosec) 30°)`


`(cos 45°)/(sec 30°+text(cosec) 30°)`




`=(sqrt3)/(2sqrt2(sqrt3+1))xx(2sqrt2(sqrt3-1))/ (2sqrt2(sqrt3+1))`





(iv) `(sin30°+tan45°-text(cosec) 60°)/(Sec30°+cos60°+cot45°)`


`(sin30°+tan45°-text(cosec) 60°)/(Sec30°+cos60°+cot45°)`







(v) `(5cos^2\60°+4sec^2\30°-tan^2\45°)/(sin^2\30°+cos^2\30°)`







Question – 2 - Choose the correct option and justify your choice:

(i) `(2tan30°)/(1+tan^2\30°)=?`

(A) sin 60o, (B) cos 60o, (C) tan 60o, (D) sin 30o

Solution: (A) sin 60o






(ii) `(1-tan^2\45°)/(1+tan^2\45°)=?`

(A) tan 90o, (B) 1, (C) sin 45o, (D) 0

Solution: (D) 0




(iii) Sin 2A = 2 Sin A is true when A = ?

(A) 0o, (B) 30o, (C) 45o, (D) 60o

Solution: (A) 0o

`Sin 0° = 0` and `Sin 2 xx 0° = Sin 0° = 0`

`Sin 30° =1/4` But `Sin 2 xx 30° = Sin 60°` is not equal to Sin 30°. The same holds true for sin 45°.

(iv) `(2tan30°)/(1-tan^2\30°)=?`

(A) cos 60o, (B) sin 60o, (C) tan 60o, (D) sin 30o

Solution: (C) tan 60o






Question 3: If tan `(A + B) = sqrt3` and `tan(A-B)=1/sqrt3`, 0°< A + B ≤ 90°, A > B; find A and B.

Solution: We know;

`tan 60° = sqrt3`

Hence, `A + B = 60°`



Hence, A – B = 30°

Adding equation (1) and (2), we get;


Or, `2A=90°`

Or, `A=45°`

So, `B=60°-45°=15°`

Question – 4 - State whether the following are true or false. Justify your answer.

  • Sin (A+B) = Sin A + Sin B

    Solution: False; this can be proved by assuming different values for A and B.
  • The value of sin θ increases as θ increases.

    Solution: True, the value of sin θ increases from zero for zero degree and goes up to 1 for 90 degree.
  • The value of cos θ increases are θ increases.

    Solution: False, the value of cos decreases from one to zero.
  • Sin θ = Cos θ for all values of θ.

    Solution: False, values of sin and cos are equal only for 45 degree.
  • Cot A is not defined for A = 0°

    Solution: True, refer to values for trigonometric ratios.

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