trigonometric ratios and identity Model Questions & Answers, Practice Test for ssc mts paper 1 2023

Answer: (a)

In 1 min = 60s, distance travelled by the wheel

= 12 × Its circumference

= 12 × 2 π r

∴ In 1 s distance travelled by the wheel

= ${12 × 2 π r}/{60} = 2/5$ π r

∵ Angle = ${Ram}/{Radius} = {2/5 π r}/r = 2/5 π$

Which is the required angle.

Answer: (a)

tan 8 θ = cot 2 θ ⇒ tan 8 θ = tan (90 - 2 θ)

⇒ 8 θ = 90 - 2 θ ⇒ θ = 9°

∴ tan 5 θ ⇒ tan 45° = 1

Answer: (c)

In ΔABC, if ∠ C is 90°, then

∠A + ∠B = 180° - 90° = 90°

then, cos(A + B) + sin (A + B)

= cos 90° + sin 90°

= 0 + 1 = 1

Answer: (c)

Now, $(sin x - cos x)^2 = (sin^2 x + cos^2 x)$ - 2 sin x cos x

= 1 - 2 $(1/2)$ (∵ sin x cos x = $1/2$, given)

Answer: (b)

cos x + sec x = 2 ......(i)

On squaring both sides, we get

$cos^2 x + sec^2 x$ + 2 = 4

⇒ $cos^2 x + sec^2 x$ = 2 ......(ii)

On cubing equation (i), we get

$cos^3 x + sec^3 x$ + 3 (cos x + sec x) = 8

⇒ $cos^3 x + sec^3 x +$ (3 × 2) = 8

⇒ $cos^3 x + sec^3$ x = 2 .....(iii)

Similarly, when we multiply n in power both sides,

$cos^n x + sec^n x = 2$

Alternate Method

of we put x = 90°

then cos 90° + sec 90° = 1 + 1 =2

Similarly $cosec^h x + sec^h x$

= $cosec^h 90° + sec^h 90°$

= 1 + 1 = 2