Question

Find the value of Sec A (1 − Sin A) (Sec A + tan A)​

Answer 1

Make me brianliest pls

Answer 2

$\bf\fbox\green{ \: Answer}$

Given that

${\underline{\boxed{\large{\rm{ sec A (1 − sin A) (sec A + tan A)}}}}}$

Remember that

$\bf\fbox\red{1+tan²A = sec²A}$

$\bf\fbox\purple{sec²A - tan²A = 1}$

$\bf\fbox\green{(secA+tanA)(secA-tanA)=1}$

$secA + tanA = \frac{1}{ (secA-tanA)}$

Take it as eq (1)

Now , as per the given question

$sec A (1 − sin A) (sec A + tan A)$

Multiply sec A with ( 1 - sin A) and also substitute eq (1) for (sec A + tan A )

So , you would be left with the following

$\frac{secA - secAsinA}{secA - tanA}$

Now , remember that

$\bf\fbox\pink{secA \: sinA = tanA}$

Take it as eq (2)

and substitute it in main equation

Now, your main equation would be like

$\frac{secA - tanA}{secA - tanA}$

and the answer is therefore 1 after cancelling

${\underline{\boxed{\large{\rm{Answer \: = 1}}}}}$

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