trigonometric ratios and identities Model Questions & Answers, Practice Test for ssc cgl tier 1 2024

Answer: (a)

Given, cosec θ = $p/q$

b = $√{p^2 - q^2}$

In ΔABC,

tan θ = $q/√{p^2 - q^2}$

⇒ $√{p^2 - q^2}$. tan θ = q

Answer: (c)

1.As, sec ∝ = (- ∞, - 1] U [1, ∞)

∴ sec ∝ ≠ ± $1/4$

2. tan β = (- ∞, ∞) tan β = 20

3. As, cosec ∝ = (-∞, -1]U[1, ∞)

∴ cosec ∝ ≠ ± $1/2$

4. As cos δ = [-1, 1]

∴ cos δ ≠ ± 2.

Answer: (c)

cot 15° cot 20° cot 70° cot 75°

= tan (90° - 15°) tan (90° - 20°) cot 70° cot 75°

= tan 75° tan 70° $1/{tan 70°} . 1/{tan 75°}$ = 1

Answer: (c)

Given, a cos θ - b sin θ = c

On squaring both sides, we get

$a^2 cos^2 θ + b^2 sin^2 θ - \text"2ab cos θ sin θ" = c^2$

⇒ $a^2 (1 - sin^2 θ) + b^2(1 - cos^2 θ) - \text"2ab sin θ cos θ" = c^2$

⇒ $a^2 + b^2 - c^2 = a^2 sin^2 θ + b^2 cos^2 θ + \text"2ab sin θ cos θ"$

⇒ $(\text"a sin θ + b cos θ")^2 = a^2 + b^2 - c^2$

⇒ a sin θ + b cos θ = ± $√{a^2 + b^2 - c^2}$

Answer: (d)

Given that,

x cos 60° + y cos 0° = 3

⇒ $x/2$ + y = 3

⇒ x + 2y = 6 .......(i)

and 4x sin 30° - y cot 45° = 2

⇒ 4x × $1/2$ - y . 1 = 2

⇒ 2x - y = 2 .......(ii)

On solving equations (i) and (ii), we get x = y - 2.