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If sec A tan A=p,then find the value of cosec A?
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If sec A tan A=p,then find the value of cosec A?
SecA+tanA=p ----------------------------(1)
∵, sec²A-tan²A=1
or, (secA+tanA)(secA-tanA)=1
or, secA-tanA=1/p -----------------------(2)
Subtracting (2) from (1) we get,
2tanA=p-1/p
or, tanA=(p²-1)/2p
∴, cotA=2p/(p²-1)
Now, cosec²A-cot²A=1
=} cosec²A=1+cot²A
=} cosec²A=1+{2p/(p²-1)}²
=} cosec²A=1+4p²/(p²-1)²
=} cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²
=} cosec²A=(p⁴+2p²+1)/(p²-1)²
=} cosec²A=(p²+1)²/(p²-1)²
=} cosecA=(p²+1)/(p²-1
That's all🙂
∵, sec²A-tan²A=1
or, (secA+tanA)(secA-tanA)=1
or, secA-tanA=1/p -----------------------(2)
Subtracting (2) from (1) we get,
2tanA=p-1/p
or, tanA=(p²-1)/2p
∴, cotA=2p/(p²-1)
Now, cosec²A-cot²A=1
=} cosec²A=1+cot²A
=} cosec²A=1+{2p/(p²-1)}²
=} cosec²A=1+4p²/(p²-1)²
=} cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²
=} cosec²A=(p⁴+2p²+1)/(p²-1)²
=} cosec²A=(p²+1)²/(p²-1)²
=} cosecA=(p²+1)/(p²-1
That's all🙂
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If sec A tan A=p,then find the value of cosec A? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sec A tan A=p,then find the value of cosec A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sec A tan A=p,then find the value of cosec A?.
If sec A tan A=p,then find the value of cosec A? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sec A tan A=p,then find the value of cosec A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sec A tan A=p,then find the value of cosec A?.
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