Question

Prove that secA - tanA.sinA
​

Answer 1

Step-by-step explanation:

secA-tanAsinA

=1/cosA-sin²A/cosA

=1-sin²A/cosA

=cos²A/cosA

=cosA

Answer 2

Solution →

LHS →

= Sec A - tan A . Sin A

$\frac{1}{cos \: a} - \frac{sin \: a}{cos \: a} \times sin \: a$

$\frac{1}{cos \: a} - \frac{ {sina}^{2} }{cos \: a} \\ \frac{1 - {sin}^{2}a }{cos \: a}$

We know that →

• Sin² a + Cos²a = 1
• cos²a = 1-sin²a

So ,

$\frac{ {cos}^{2} a}{cos \: a}$

$\boxed{\huge{=cos\:a}}$ RHS

Hence Proved !!

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