Simplify the expression-sinA - sinB-cosA - cosB - cosA- cosB-sinA - sinB

SinA sinB/cosA + cosB + cosA cosB/sinA + sinB = (sinA sinB) (sinA + sinB) + (cosA cosB) (cosA + cosB)/(cosA + cosB) (sinA + sinB) =sin^2 A sin^2 B ...

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Standard X

Mathematics

Trigonometric Ratios

Simplify the ...

Question

Simplify the expression:
$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$

- 1

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Solution

The correct option is B
0

$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$

$= \frac{(s i n A - s i n B) (s i n A + s i n B) + (c o s A - c o s B) (c o s A + c o s B)}{(c o s A + c o s B) (s i n A + s i n B)} = \frac{s i n^{2} A - s i n^{2} B + c o s^{2} A - c o s^{2} B}{(c o s A + c o s B) (s i n A + s i n B)} = \frac{s i n^{2} A + c o s^{2} A - (s i n^{2} B ‘ + c o s^{2} B)}{(c o s A + c o s B) (s i n A + s i n B)} = \frac{1 - 1}{(c o s A + c o s B) (s i n A + s i n B)} = 0$

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Similar questions

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

Q. Prove that :

\frac{sin A - sin B}{cos A + cos B} + \frac{cos A - cos B}{sin A + sin B} = 0

{(\frac{c o s A + c o s B}{s i n A - s i n B})}^{2014} + {(\frac{s i n A + s i n B}{c o s A - c o s B})}^{2014} = . . . . . . . . . . .

sin a + sin b = - \frac{21}{65}, cos a + cos b = - \frac{27}{65} \Rightarrow cos (\frac{a - b}{2}) =

Q. Assertion :

{(\frac{cos A + cos B}{sin A - sin B})}^{n} + {(\frac{sin A + sin B}{cos A - cos B})}^{n}

= 2 {cot}^{n} (\frac{A - B}{2})

n

is even

= 0

n

is odd. Reason:

\frac{cos A + cos B}{sin A - sin B} = cot \frac{A - B}{2}

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Simplify the expression: sinA−sinBcosA+cosB+cosA−cosBsinA+sinB

The correct option is B 0 sinA−sinBcosA+cosB+cosA−cosBsinA+sinB =(sinA−sinB)(sinA+sinB) + (cosA−cosB)(cosA+cosB)(cosA+cosB)(sinA+sinB)=sin2A−sin2B+cos2A−cos2B(cosA + cosB)(sinA + sinB)=sin2A + cos2A − (sin2B ‘+ cos2B)(cosA + cosB)(sinA + sinB)=1−1(cosA + cosB)(sinA + sinB)=0

Simplify the expression:
$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$