Question

find the value of k if tan (15 minus k)degrees equals cot (2k + 60)degrees.

Answer this with step by step solutions.

Answer 1

Solution :-

tan (15 - k) = cot (2k + 60)

To find the value of k we need to equate angles of both sides

To equate angles the trignometric ratios on both sides should be same

To make same trigonometric ratios we should use trignometric ratios of complementary angles concept

⇒ tan (15 - k) = cot (2k + 60)

⇒ cot [ 90 - (15 - k) ] = cot (2k + 60)

[ Because tan θ = cot (90 - θ) ,here θ = 15 - k ]

⇒ cot (90 - 15 + k) = cot (2k + 60)

⇒ cot (75 + k) = cot (2k + 60)

Comparing on both sides

⇒ 75 + k = 2k + 60

⇒ 75 - 60 = 2k - k

⇒ 15 = k

⇒ k = 15

Therefore the value of k is 15.

Answer 2

Answer:

k = 15

Step-by-step explanation:

Given :

tan ( 15 - k ) = cot ( 2 k + 60 )

Using complementary formula :

i.e. tan ( 90 - Ф ) = cot Ф

cot ( 90 - ( 15 - k ) ) = cot ( 2 k + 60 )

On comparing we get :

90 - ( 15 - k ) = ( 2 k + 60 )

90 - 15 + k = 2 k + 60

75 + k = 2 k + 60

k = 75 - 60

k = 15.

Hence the value of 'k' is 15°