Question

Show that cos 16 + sin 16 ÷ cos 16 - sin 16 = tan 61

Answer 1

Answer:

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Answer 2

Answer:

cos 16 + sin 16 ÷ cos 16 - sin 16 = tan 61

Step-by-step explanation:

Given that  cos 16 + sin 16 ÷ cos 16 - sin 16 = tan 61

taking LHS  cos 16 + sin 16 ÷ cos 16 - sin 16

          rewrite as 16 = 61-45

        = cos (62 - 45) + sin (61 - 45) ÷ cos (61 - 45) - sin(61 - 45)

we know that cos (a - b) = (cos a) (cos b) + (sin a) (sin b)

                        sin(a - b) = (sin a) (cos b) - (cos a) (sin b)

using the above formula the equation can be rewritten as

=>((cos 61)(sin 45)+(sin 61)(sin 45)+(sin 61)(cos 45)+(cos 61)(sin 45)) ÷ (cos 61)((cos 45)+(sin 61)(sin 45)-(sin 61)(cos 45)- (cos 61)(sin 45))

=>((cos 61)(cos 45)+(sin 61)(sin 45)+(sin 61)(cos 45) - (cos 61)(sin 45))  ÷ ((cos 61)(cos 45)+ (sin 61)(sin 45) - (sin 61)(cos 45) +(cos 61)(sin 45))

after cancelling the terms the equation is:

=>(1/√2) (sin 61) + (1/√2) (sin 61)  ÷(1/√2) (cos 61) + (1/√2) (cos 61)

=> ((2 sin 61)/√2)÷((2 cos 61)/√2)

=>(2 sin 61) ÷ (2 cos 61)

=> sin 61÷cos 61

=>tan 61 (hence proved)

To know more about trignometric equations visit the link below:

https://brainly.in/question/17745887

https://brainly.in/question/7623361