State true or false-cos A -1-sin A -tan A -cos AA- FalseB- True

The correct option is A False L.H.S = cos A/1+sin A + tan A =cos A/1+sin A×1 sin A/1 sin A + tan A =c̸o̸s̸ ̸A̸(̸1̸ ̸s̸i̸n̸ ̸A̸)̸/cos^2 A+sin A/cos A =1 s̸i̸ ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

State true or...

Question

State true or false:

$\frac{c o s A}{1 + s i n A} + t a n A = c o s A$

True

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False

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Solution

The correct option is B
False

L.H.S $= \frac{c o s A}{1 + s i n A} + t a n A$

$= \frac{c o s A}{1 + s i n A} \times \frac{1 - s i n A}{1 - s i n A} + t a n A$

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

$= \frac{1 - / s i n A + / s i n A}{c o s A}$

$= \frac{1}{c o s A} = s e c A \neq R . H . S$

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State true or false: cos A1+sin A+tan A=cos A

The correct option is B False L.H.S =cos A1+sin A+tan A =cos A1+sin A×1−sin A1−sin A+tan A =/cos A(1−sin A)cos2 A+sin Acos A =1−/sin A+/sin Acos A =1cos A=sec A≠R.H.S

State true or false:

$\frac{c o s A}{1 + s i n A} + t a n A = c o s A$