Question

cosec ^3 30° cos 60° tan^3 45° sin^2 90° sec² 45° cot 30°​

Answer 1

Answer:

To evaluate :-

cosec³ 30° cos 60° tan³ 45° sin² 90° sec² 45° cot 30°

Salutation :-

cosec³ 30° cos 60° tan³ 45° sin² 90° sec² 45° cot 30°

= ( 2 )³ × ( 1 / 2 ) × ( 1 )³ × ( 1 )² × ( √2 )² × ( √3 )

= 8 × 1 / 2 × 1 × 1 × 2 × √3

= 8 × √3

= 8√3

______________________________

Since ,

cosec30° = 2

cos60° = 1 / 2

tan45° = 1

sin90° = 1

sec45° = √2

cot30° = √3

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Answer 2

Step-by-step explanation:

first we have to find all trigonometric values

cosec 30° = 2

so

cosec ^3 30° = (2)^3 = 8 ........(1)

cos 60° = 1/2 ........(2)

tan 45° = 1

so

tan ^3 45° = ( 1)^3 = 1 ..........(3)

sin 90° = 1

so

sin^2 90° = (1)^2 = 1 ............(4)

sec 45° = √2

so

sec^2 45° = (√2)^2 = 2 ..........(5)

cot 30° = √3 .........(6)

now put all values in question

cosec^3 30° cos 60° tan^3 45° sin ^2 90° sec^2 45° cot 30°

= 8 * 1/2 * 1 * 1 * 2 * √3

= 4* 2 *√3

= 8 * √3

= 8√3