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CBSE Class 10 Answered

mathematics
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Asked by coolbhavanakothari08 | 02 Jun, 2020, 08:58: PM
answered-by-expert Expert Answer
Question: If tan2theta + cot2theta = 2 then tan3theta + cot3theta is equal to:
Solution:
As per the question, it is given that
tan squared theta plus c o t squared theta equals 2 space... space left parenthesis i right parenthesis
rightwards double arrow tan squared theta plus c o t squared theta plus 2 minus 2 equals 2
rightwards double arrow tan squared theta plus c o t squared theta plus 2 space tan theta space c o t theta minus 2 equals 2
rightwards double arrow open parentheses tan theta plus c o t theta close parentheses squared equals 4
rightwards double arrow space tan theta thin space plus space c o t theta space equals space 2 space... space left parenthesis i i right parenthesis
C o n s i d e r comma
tan cubed theta plus c o t cubed theta
equals open parentheses tan theta space plus space c o t theta close parentheses open parentheses tan squared theta plus c o t squared theta minus 1 close parentheses
equals open parentheses 2 close parentheses open parentheses 2 minus 1 close parentheses
equals 2
H e n c e comma space tan cubed theta plus c o t cubed theta equals 2
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square root of fraction numerator 1 plus sin empty set over denominator 1 minus sin empty set end fraction end root plus square root of fraction numerator 1 minus sin empty set over denominator 1 plus sin empty set end fraction end root equals 2 s e c empty set
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