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PSYCHO15rus [73]
3 years ago
10

If sinA+cosecA=3 find the value of sin2A+cosec2A​

Spanish
1 answer:
VMariaS [17]3 years ago
8 0

Answer:

\sin^2 A + cosec^2A = 7

Explanation:

Given

\sin A+cosec\ A=3

Required

Find \sin^2A + cosec^2A

\sin A+cosec\ A=3

Square both sides

(\sin A+cosec\ A)^2=3^2

(\sin A+cosec\ A)(\sin A+cosec\ A)=9

Open brackets

\sin^2 A + 2\sin A\ cosec\ A + cosec^2A = 9

In trigonometry:

cosec\ A = \frac{1}{\sin A}

So, we have:

\sin^2 A + 2\sin A *\frac{1}{\sin A} + cosec^2A = 9

\sin^2 A + \frac{2\sin A}{\sin A} + cosec^2A = 9

\sin^2 A + 2 + cosec^2A = 9

Collect like terms

\sin^2 A + cosec^2A = 9-2

\sin^2 A + cosec^2A = 7

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