Question

7 sin^2 30° +6cosec^2 60°-cot^2 45°/sin^2 60° + cos^2 60°​

Answer 1

Step-by-step explanation:

7 sin^2 30° +6cosec^2 60°-cot^2 45°/sin^2 60° + cos^2 60

Through the trigonometry table,

7(1/2)^2 + 6(2/√3)^2 - (1)^2/(√3/2)^2 + (1/2)^2

7/4 + 24/3 - 4/3 + 1/4

8/4 + 20/3

2 + 20/3

(6 + 20)/3

26/3

Answer 2

Given,

7 sin² 30° +6cosec² 60°-cot² 45°/sin² 60° + cos² 60°

To find,

Value of the given equation

Solution,

According to the trignometric table of values;

Sin 30 = 1/2

cosec 60 = 2/√3

cot 45 = 1

sin 60 = √3/2

cos 60 = 1/2

Putting in the values

7(1/2)² + 6(2/√3)² - (1)²/(√3/2)² + (1/2)²

= 7/4 + 24/3 - 4/3 + 1/4

= 8/4 + 20/3

= 2 + 20/3

= (6 + 20)/3

= 26/3

So the value of 7 sin² 30° +6cosec² 60°-cot² 45°/sin² 60° + cos² 60°​ is equal to 26/3