Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Introduction to Trigonometry and its Applications:

Exercise 8.2

Very Short Answer Type Questions (Q. No. 1-7)

Write whether True or False and justify your answer.

Question. 2 The value of the expression (cos² 23° - sin² 67°) is positive.

Solution. False

Question. 3 The value of the expression (sin 80° - cos 80°) is negative.

Solution. False

We know that for domain, 0° £ q £90° the value of sinq is increasing and that of cosq is decreasing .

∴        sin80° - cos80°> 0

So, the value of the given expression is positive.          

Question. 5 If cos A + cos² A = 1, then sin² A + sin⁴ A = l

Solution. True

Given, cosA + cos² A = 1

⟹     cos A = 1 - cos²A

⟹     cos A = sin² A              [∵ sin² A = 1 − cos²A]

⟹     cos² A = sin⁴ A             [Squaring both sides]

⟹     1 - sin² A = sin⁴ A         [∵ cos² A = 1 - sin² A]

⟹     sin² A + sin⁴ A = 1      

Question. 6 (tanθ + 2) (2 tanθ + 1) = 5 tanθ + sec²θ

Solution. False

LHS = (tanθ + 2)(2tanθ + 1)

        =2 tan²θ + 4 tanθ + tanθ + 2

        =2 (sec²θ -1) + 5 tanθ + 2         [∵ sec²θ -tan²θ = 1]

        =2sec²θ + 5tanθ ≠ RHS

Question. 7 If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing.

Solution. False

Let BC be the tower and DB = x be the length of initial shadow and DA = y be the the increase in length of shadow.

Also, let the angle of elevation of the sun changes from θ₁ to θ₂ with the increase in the length of shadow from x to (x + y).

Here, θ₁ is the exterior angle of ΔTSD

Therefore, θ₁ > θ₂.

Hence, the angle of elevation of the Sun is also increasing with an increase in the length of shadow.