Evaluate: sin 35 ° · sin 55 ° - cos 35 ° · cos 55 °

sin 35 ° · sin 55 ° - cos 35 ° · cos 55 ° = sin 35 ° · cos 90 ° - 55 ° - cos 35 ° · sin 90 ° - 55 ° [ cos ( 90 ° - θ ) = sin θ ] = sin 35 ° · cos 35 ° - cos 35 ° · sin 35 ° = 0 Therefore, the required answer is 0 .

Find the value of tan 45 ° cosec 30 ° + sec 60 ° cot 45 ° - 5 sin 90 ° 2 cos 0 ° .

We need to find the value of tan 45 ° cosec 30 ° + sec 60 ° cot 45 ° - 5 sin 90 ° 2 cos 0 ° . We know that, tan 45 ° = 1 , cosec 30 ° = 2 , sec 60 ° = 2 , cot 45 ° = 1 , sin 90 ° = 1 , cos 0 ° = 1 Substituting the values of specific angles, we get, tan 45 ° cosec 30 ° + sec 60 ° cot 45 ° - 5 sin 90 ° 2 cos 0 ° = 1 2 + 2 1 - 5 × 1 2 × 1 = 1 2 + 2 1 - 5 2 = 1 + 4 - 5 2 = 5 - 5 2 = 0 2 = 0 Therefore, the value of tan 45 ° cosec 30 ° + sec 60 ° cot 45 ° - 5 sin 90 ° 2 cos 0 ° is 0 .

Evaluate sin 15 ° . sec 75 °

Given: sin 15 ° sec 75 ° Using the concept of complementary angles, we know that sec ( 90 ° - θ ) = cosec θ ⇒ sec 75 ° = sec ( 90 ° - 15 ° ) = cosec 15 ° Also, we know that, cosec θ = 1 sin θ ⇒ sin 15 ° . sec 75 ° = sin 15 ° × 1 sin 15 ° = 1 Hence, the required answer is 1 .