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if 7{cosec(a)-1}=3cot(a),then show 3{cosec(a)+1}=7cot(a)

if 7{cosec(a)-1}=3cot(a),then
show 3{cosec(a)+1}=7cot(a)

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Hello student,
7{cosec(a)-1} = 3cot(a)
So, we have 7 cosec a – 3 cot a = 7
squaring both sides,
(7 cosec a – 3 cot a)2 = 72
so, (7 cosec a)2 + (3 cot a)2 – 2(7 cosec a) (3 cot a) = 49
49 cosec2a + 9 cot2a – 42 cosec a cot a = 49
This gives 49 (1 + cot2a) + 9 (cosec2a – 1) – 42 cosec a cot a = 49
49 cot2a + 9 cosec2a – 42 cosec a cot a = 9
This can be written as
(7 cot a – 3 cosec a)2 = 9
so, (7 cot a – 3 cosec a) = 3

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