Question

The value of [(secA +tan A)(1-sinA)] is equal to
a) tan? A
b) sinA
c) cosA
d) sinA​

Answer 1

Answer:

Step-by-step explanation:

According to the problem statement, we are given an expression as (secA+tanA)(1−sinA). Now, by using the reciprocal identities secθ=1cosθ and tanθ=sinθcosθ respectively, we get the simplified expression as:

⇒(1cosA+sinAcosA)(1−sinA)

Since the denominator is same, so solving for the numerator, we get

⇒(1+sinAcosA)(1−sinA)

Using the algebraic identity a2−b2=(a+b)(a−b), we can also write (1−sinA)(1−sinA) as 1−sin2A. So, further simplification yields

⇒(1−sinA)(1+sinA)cosA⇒1−sin2AcosA

As we know that the sin2A+cos2A=1. So, we can rewrite 1−sin2A as cos2A. Putting it in above expression, we get

⇒cos2AcosA⇒cosA

Hence, the value of (secA + tanA) (1 – sinA) is equal to cosA.

Therefore, option (C) is correct.

Answer 2

Answer:

c opinion is correct opinion

Step-by-step explanation:

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