Question

sin 28°× sec 62° + cosec² 30°
help please?​

Answer 1

GIVEN:

Trigonometric expressions i.e, sin 28°× sec 62° + cosec² 30°

To Find:

The value of the expression sin 28°× sec 62° + cosec² 30°.

Procedure:

• The expression is sin 28°×sec 62°+cosec² 30°.

• The above expression can also be written as (sin28°/cos62°)+cosec² 30°.

• According to the trigonometric properties secx=(1/cosx) .[ Sine , Cos, Tan trigonometric functions are the inverses of the trigonometric functions Cosec , Sec and Cot respectively!

• The above expression can be furtherly modified as follows:

         (sin28°/sin28°)+cosec² 30°.

•  Since it follows the trigonometric properties i.e, sin(90-x)=cosx.

         [ Above relation is Taken from the  trigonometric relations ]

• Therefore, the expression finally changed to 1+cosec² 30°

        (since sin28°/sin28°=1 as they are equal values)

• Since the  value of cosec30°=2, Substitute the value in the modified expression for the final result

     => 1+cosec² 30°= 1+4=5 .

Therefore, The value of the expression sin 28°× sec 62° + cosec² 30° =5.