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Standard Values of Trigonometric Ratios

SinA+sinB=a a...

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SinA+sinB=a and cosA-cosB=b then tan(A-B)/2?

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Prove that:
(i) $\frac{s i n A + s i n 3 A}{c o s A - c o s 3 A} = c o t A$
(ii) $\frac{s i n 9 A - s i n 7 A}{c o s 7 A - c o s 9 A} = c o t 8 A$
(iii) $\frac{s i n A - s i n B}{c o s A - c o s B} = t a n \frac{A - B}{2}$
(iv) $\frac{s i n A + s i n B}{s i n A - s i n B} t a n (\frac{A + B}{2}) c o t \frac{A + B}{2}$
(v) $\frac{c o s A + c o s B}{c o s B - c o s A} = c o t \frac{A + B}{2} c o t \frac{A - B}{2}$

If cos(A-B) = 3/5 and tanA*tanB = 2 then

(a) cosA*cosB= 1/5 (c) cos(A+B)= -1/5

(b) sinA*sinB= 2/5 (d) sinA*sinB=4/5

sin A + sin B = a

cos A + cos B = b

then find the value of

cos (A - B)

sin A + sin B = α

cos A + cos B = β

then, write the value of

tan (\frac{A + B}{2})

sin A = sin B

cos A = cos B

sin \frac{A - B}{2} =

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