Let a-b-c-d A-B-C- D - R- If A a - B b - C c - D d- then - aA - bB - cC - dD - a-b-c-d - A-B-C-D is equal to

The correct option is D 1 A/a = Bb = Cc = Dd = K = √(a× ak)+√(b× bk) +√(c× ck) +√(d× dk)√(a+b+c+d)√(ak + bk + ck +dk) = a√(k) + b√(k) + c√(k ...

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Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

Let a,b,c,d...

Question

Let $a, b, c, d A, B, C, D ϵ R^{*}$ . If $\frac{A}{a} = \frac{B}{b} = \frac{C}{c} = \frac{D}{d}$ , then $\frac{\sqrt{a A} + \sqrt{b B} + \sqrt{c C} + \sqrt{d D}}{\sqrt{a + b + c + d} \sqrt{A + B + C + D}}$ is equal to

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Solution

The correct option is D $1$
$\frac{A}{a} = \frac{B}{b} = \frac{C}{c} = \frac{D}{d} = K$

$= \frac{\sqrt{a \times a k} + \sqrt{b \times b k} + \sqrt{c \times c k} + \sqrt{d \times d k}}{\sqrt{a + b + c + d} \sqrt{a k + b k + c k + d k}}$

$= \frac{a \sqrt{k} + b \sqrt{k} + c \sqrt{k} + d \sqrt{k}}{\sqrt{k} \sqrt{a + b + c + d} \sqrt{a + b + c + d}}$

$= \frac{\sqrt{k} (a + b + c + d)}{\sqrt{k} (a + b + c + d)} = 1$

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Let a,b,c,d A,B,C, D ϵR∗. If Aa=Bb=Cc=Dd, then √aA+√bB+√cC+√dD√a+b+c+d√A+B+C+D is equal to

The correct option is D 1Aa=Bb=Cc=Dd=K=√a×ak+√b×bk+√c×ck+√d×dk√a+b+c+d√ak+bk+ck+dk=a√k+b√k+c√k+d√k√k√a+b+c+d√a+b+c+d=√k(a+b+c+d)√k(a+b+c+d)=1

Let $a, b, c, d A, B, C, D ϵ R^{*}$ . If $\frac{A}{a} = \frac{B}{b} = \frac{C}{c} = \frac{D}{d}$ , then $\frac{\sqrt{a A} + \sqrt{b B} + \sqrt{c C} + \sqrt{d D}}{\sqrt{a + b + c + d} \sqrt{A + B + C + D}}$ is equal to