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 .

Find the value of sin 90 ° + cos 60 ° + cos 45 ° × sin 30 ° + cos 0 ° - cos 45 ° .

We need to find the value of sin 90 ° + cos 60 ° + cos 45 ° × sin 30 ° + cos 0 ° - cos 45 ° . We know that, sin 90 ° = 1 , cos 60 ° = 1 2 , cos 45 ° = 1 2 , sin 30 ° = 1 2 , cos 0 ° = 1 . Substituting the values of specific angles, we get, sin 90 ° + cos 60 ° + cos 45 ° × sin 30 ° + cos 0 ° - cos 45 ° = 1 + 1 2 + 1 2 × 1 2 + 1 - 1 2 = 3 2 + 1 2 3 2 - 1 2 = 3 2 2 - 1 2 2 = 9 4 - 1 2 = 7 4 . Therefore, the value of sin 90 ° + cos 60 ° + cos 45 ° × sin 30 ° + cos 0 ° - cos 45 ° is 7 4 .

What are the minimum and maximum values of sin θ ? ( 0 ° ≤ θ ≤ 90 ° )

We need to find the minimum and maximum values of sin θ . We know that the value of θ varies from 0 ° to 90 ° . Let us write a few specific values sin θ . We know that, sin 0 ° = 0 , sin 30 ° = 1 2 , sin 45 ° = 1 2 , sin 60 ° = 3 2 , sin 90 ° = 1 We can see that the value of sin θ increases as θ varies from 0 ° to 90 ° . Minimum value of sin θ is 0 , when θ = 0 ° . Maximum value of sin θ is 1 when θ = 90 ° .