Question

cos^2A + sec^2A - {tan^2A - sin^2A}​

Answer 1

Required Answer:-

We have to evaluate:

• cos² A + sec² A - (tan² A - sin² A)

Now opening the parentheses,

= cos² A + sec² A - tan² A + sin² A

Bring the appropriate ratios near to match the identities$:$

• sin² A + cos² A = 1
• sec² A - tan² A = 1

It will be,

= cos² A + sin² A + sec² A - tan² A

= 1 + 1

= 2

Hence:

After evaluating and solving using identities, we will get the answer as 2.

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Co-function or periodic identities:

• sin (90°−x) = cos x
• cos (90°−x) = sin x
• tan (90°−x) = cot x
• cot (90°−x) = tan x
• sec (90°−x) = csc x
• cosec (90°−x) = sec x

Basic sum Identities:

• sin² A + cos² A = 1
• cosec² A - cot² A = 1
• sec² A - tan² A = 1

Answer 2

We have to evaluate:

cos² A + sec² A - (tan² A - sin² A)

Now opening the parentheses,

= cos² A + sec² A - tan² A + sin² A

Bring the appropriate ratios near to match the identities::

sin² A + cos² A = 1

sin² A + cos² A = 1sec² A - tan² A = 1

= cos² A + sin² A + sec² A - tan² A= 1 + 1= 2

Hence:

After evaluating and solving using identities, we will get the answer as 2.

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Co-function or periodic identities:

sin (90°−x) = cos xcos (90°−x) = sin xtan (90°−x) = cot xcot (90°−x) = tan xsec (90°−x) = csc xcosec (90°−x) = sec xBasic sum Identities:sin² A + cos² A = 1