Question

Find the value of

(i) cos 15 (ii) sin 105 (iii) tan 105​

Answer 1

Answer:

cos 15 = √3 + 1 ÷ 2√2

sin 105 = √3 + 1 ÷ 2√2

tan 105 = - (√3 + 1 )÷ (√3 - 1 )

Step-by-step explanation:

cos 15 = cos( 45 - 30 )

cos( 45 - 30 ) = cos(45) cos(30) + sin(45) sin(30)

cos( 45 - 30 ) = ( 1/√2 ) (√3/2) + ( 1/√2 ) ( 1/2)

cos( 45 - 30 ) = √3 + 1 ÷ 2√2

cos 15 = √3 + 1 ÷ 2√2

sin 105 = sin ( 90 + 15 )

sin 105 = cos 15

sin 105 = √3 + 1 ÷ 2√2

tan 105 = tan ( 90 + 15 )

tan 105 = - cot 15

now cot 15 = cos 15 / sin 15

sin 15 = sin( 45 - 30 )

sin( 45 - 30 ) = sin(45) cos(30) - cos(45) sin(30)

sin( 45 - 30 ) = ( 1/√2 ) (√3/2) - ( 1/√2 ) ( 1/2)

sin( 45 - 30 ) = √3 - 1 ÷ 2√2

sin(15) = √3 - 1 ÷ 2√2

cot 15 = cos 15 / sin 15

cot 15 = ( √3 + 1 ÷ 2√2 ) ÷ ( √3 - 1 ÷ 2√2 )

cot 15 = (√3 + 1 )÷ (√3 - 1 )

tan 105 = - cot 15

tan 105 = - (√3 + 1 )÷ (√3 - 1 )