If cosec A - B -2-3- A - B -2-30- A - B - 90-Find A and B-A- 10- 50-B- 30- 30-C- 25- 35-D- 45- 15-

The correct option is D 45o, 15o If A+B lies in this range 0^∘ A+B ≤ 90^∘ cosec(A+B)=2/√(3) only when A+B=60^∘ ........(1) sec(A B)=2/√(3), only when A B=30^∘ ...

If cosec A + ...

Question

If $c o s e c (A + B) = \frac{2}{\sqrt{3}}$ , sec(A-B)= $\frac{2}{\sqrt{3}}$ ,
$0^{\circ} < A + B \leq 90^{\circ}$ ,
Find A and B.

10^o, 50^o

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45^o, 15^o

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30^o, 30^o

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25^o, 35^o

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Solution

The correct option is D
45^o, 15^o

If A+B lies in this range $0^{\circ} < A + B \leq 90^{\circ}$
$c o s e c (A + B) = \frac{2}{\sqrt{3}}$ only when $A + B = 60^{\circ}$ ........(1)
sec(A-B)= $\frac{2}{\sqrt{3}}$ , only when $A - B = 30^{\circ}$ ........(2)
By Solving equation 1 and equation 2
$A = 45^{\circ}$ and $B = 15^{\circ}$

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The correct option is D 45o, 15o If A+B lies in this range 0∘<A+B≤90∘ cosec(A+B)=2√3 only when A+B=60∘ ........(1) sec(A-B)=2√3, only when A−B=30∘ ........(2) By Solving equation 1 and equation 2 A=45∘ and B=15∘

If $c o s e c (A + B) = \frac{2}{\sqrt{3}}$ , sec(A-B)= $\frac{2}{\sqrt{3}}$ ,
$0^{\circ} < A + B \leq 90^{\circ}$ ,
Find A and B.