Question

verify the following.
V5-1 TT i) sin18° = sin 2IT - Cos 72° = cos 25 11 10 4​

Answer 1

Step-by-step explanation:

sin 18°/cos 72°

Since, sin (90° - θ) = cos θ

Here, θ = 72°

sin 18°/cos 72° = sin (90° - 72°)/cos 72°

= cos 72° / cos 72°

= 1

Answer 2

Step-by-step explanation:

We will be using the trigonometric ratios of complementary angles to solve the given question.

sin (90° - θ) = cos θ

tan (90° - θ) = cot θ

sec (90° - θ) = cosec θ

(i) sin 18°/cos 72°

Since, sin (90° - θ) = cos θ

Here, θ = 72°

sin 18°/cos 72° = sin (90° - 72°)/cos 72°

= cos 72° / cos 72°

= 1

(ii) tan 26°/cot 64°

tan (90° - θ) = cot θ

Here, θ = 64°

tan 26°/cot 64° = tan (90° - 64°) / cot 64°

= cot 64°/cot 64°

= 1

(iii) cos 48° - sin 42°

Since, sin (90° - θ) = cos θ

Here, θ = 48°

cos 48° - sin 42° = cos 48° - sin (90° - 48°)

= cos 48° - cos 48°

= 0

(iv) cosec 31° - sec 59°

sec (90° - θ) = cosec θ

Here, θ = 31°

cosec 31° - sec 59° = cosec 31° - sec (90° - 31°)

= cosec 31° - cosec 31°

= 0