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    Maths-
    General
    Easy

    Question

    If sec to the power of 4 space theta plus sec squared space theta equals 10 plus tan to the power of 4 space theta plus tan squared space theta text  then  end text sin squared text end text theta =

    1. 2 over 3
    2. 3 over 4
    3. 4 over 5
    4. 5 over 6

    The correct answer is: 4 over 5

      sec to the power of 4 theta plus sec squared theta equals 10 plus tan to the power of 4 theta plus tan squared theta sec squared theta open parentheses sec squared theta plus 1 close parentheses equals 10 plus tan squared theta open parentheses tan squared theta plus 1 close parentheses sec squared theta open parentheses sec squared theta plus 1 close parentheses equals 10 plus tan squared theta open parentheses sec squared theta close parentheses sec squared theta open parentheses sec squared theta plus 1 close parentheses minus tan squared theta open parentheses sec squared theta close parentheses equals 10 sec squared theta open parentheses sec squared theta plus 1 minus tan squared theta close parentheses equals 10 sec squared theta open parentheses 1 plus 1 close parentheses equals 10 space space space space space space space space space space space space space space space because open parentheses sec squared theta minus tan squared theta equals 1 close parentheses 2 sec squared theta equals 10 therefore sec squared theta equals 5 therefore fraction numerator 1 over denominator cos squared theta end fraction equals 5 therefore cos squared theta equals 1 fifth W e space k n o w space t h a t comma sin squared theta plus cos squared theta equals 1 therefore sin squared theta equals 1 minus cos squared theta equals 1 minus 1 fifth equals fraction numerator 5 minus 1 over denominator 5 end fraction equals 4 over 5

      We can also find the answer using pythagoras theorem after getting the value of sectheta

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