Question

simplyify secA(1-sinA)(secA+tanA)​

Answer 1

Topic

Trigonometry

To Simplify

secA( 1 - sinA )( secA + tanA )

Solution

Multiply secA with ( 1 - sinA )

[ ( secA × 1 ) - ( secA × sinA ) ]( secA + tanA )

As we know that,

$\sf {secA = \dfrac{1}{cosA}}$

We can write,

$\sf {[ secA - ( \dfrac{1}{cosA} \times sinA ) ]( secA + tanA ) }$

As we know,

$\sf {\dfrac{sinA}{cosA} = tanA }$

We can write,

$\sf { ( secA - tanA )( secA + tanA ) }$

From formula,

( a - b )( a + b ) = a² - b²

We can write,

sec²A - tan²A

Form formula,

1 + tan²x = sec²x

1 = sec²x - tan²x

We can write,

sec²A - tan²A = 1

Answer

So, secA( 1 - sinA )( secA + tanA ) = 1

More Formulae

sin²x + cos²x = 1

1 + cot²x = cosec²x

Answer 2

Given : 

$secA (1−sinA)(secA+tanA)$

$cosA1(1−sinA) \\ (cosA1 \: + \: cosAsinA)$

$(∵secA=cosA1)$

$(cosA1−sinA)(cosA1+sinA)$

$cos2A1−sin2A$

$As, 1−sin2A=cos2A$

$cos2Acos2A =1$