Mathematics
If sin A + cosec A = 2; find the value of sin2 A + cosec2 A.
Trigonometric Identities
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Answer
sin A + cosec A = 2
Squaring both sides,
(sin A + cosec A)2 = 22
⇒ sin2 A + cosec2 A + 2 x sin A x cosec A = 4
⇒ sin2 A + cosec2 A + 2 x sin A x = 4
⇒ sin2 A + cosec2 A + 2 x x = 4
⇒ sin2 A + cosec2 A + 2 = 4
⇒ sin2 A + cosec2 A = 4 - 2
⇒ sin2 A + cosec2 A = 2
Hence, sin2 A + cosec2 A = 2.
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