Simplify cos A1-sin A-1-sin Acos A-2 A

To simplify : cos A/1+ sin A+1+ sin A/cos A=2 sec A LHS cos^2A+(1+sin A)^2/(1+ sin A)(cos A)=cos^2A+1+sin^2A+2 sin A/(1+sin A)cos A =2+2 sin A/(1+ ...

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Byju's Answer

Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Simplify cos...

Question

Simplify
$\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A$

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Solution

To simplify : $\frac{c o s A}{1 + s i n A} + \frac{1 + s i n A}{c o s A} = 2 s e c A$
LHS
$\frac{c o s^{2} A + (1 + s i n A)^{2}}{(1 + s i n A) (c o s A)} = \frac{c o s^{2} A + 1 + s i n^{2} A + 2 s i n A}{(1 + s i n A) c o s A}$
$= \frac{2 + 2 s i n A}{(1 + s i n A) c o s A} = \frac{2 (1 + s i n A)}{(1 + s i n A) c o s A} = 2 s e c A$ $[c o s^{2} A + s i n^{2} A = 1]$
LHS = RHS
Hence simplified.

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Similar questions

$\frac{c o s A}{(1 + s i n A)} + \frac{(1 + s i n A)}{c o s A} = 2 s e c A$

Q. Prove:

\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A

Q. Prove

\frac{1 + sin A}{cos A} + \frac{cos A}{1 + sin A} = 2 sec A

Q. Solve:

\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A}

= 2 sec A

Q. Solve

\frac{1 + sin A}{cos A} + \frac{cos A}{1 + sin A} = 2 sec A

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SimplifycosA1+sinA+1+sinAcosA=2secA

To simplify : cosA1+sinA+1+sinAcosA=2secALHScos2A+(1+sinA)2(1+sinA)(cosA)=cos2A+1+sin2A+2sinA(1+sinA)cosA=2+2sinA(1+sinA)cosA=2(1+sinA)(1+sinA)cosA=2secA [cos2A+sin2A=1]LHS = RHSHence simplified.

Simplify
$\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A$