Question

The value of 2 sin2A + 4 sec2 A + 5 cot2 A + 2 cos2A – 4 tan2 A – 5

cosec2 A is​

Answer 1

The value of 2sin²A + 4sec²A + 5cot²A  + 2cos²A - 4tan²A - 5cosec²A  is 1.

The options are a) 0 b) 1 c) 2 d) 3​

Explanation:

The Trigonometric identities are:

i ) sin²A + cos²A = 1

ii ) sec²A - tan² A = 1

iii ) cot²A-cosec²A = -1

Substituting these values in the given equation,

⇒  2sin²A + 4sec²A + 5cot²A  + 2cos²A - 4tan²A - 5cosec²A

By combining the values according to the trigonometric identities, the equation can be rewritten as

⇒ 2(sin²A+cos²A) + 4(sec²A-tan²A)  + 5( cot²A - cosec²A )

⇒ 2 × 1 + 4 × 1 + 5 × ( -1 )  ----------[ the values are substituted ]

⇒ 2 + 4 - 5

⇒ 6 - 5

= 1

Therefore, the value of 2sin²A + 4sec²A + 5cot²A  + 2cos²A - 4tan²A - 5cosec²A  is 1 .