if y = log tan (∏/4 + x/2)  show that dy/dx = sec x

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Asked by haroonrashidgkp | 11th Jul, 2018, 12:29: PM

Expert Answer:

begin mathsize 16px style straight y equals log open square brackets tan open parentheses straight pi over 4 plus straight x over 2 close parentheses close square brackets
dy over dx equals fraction numerator 1 over denominator tan open parentheses straight pi over 4 plus straight x over 2 close parentheses end fraction cross times sec squared open parentheses straight pi over 4 plus straight x over 2 close parentheses cross times 1 half
dy over dx equals fraction numerator cos open parentheses straight pi over 4 plus straight x over 2 close parentheses over denominator sin open parentheses straight pi over 4 plus straight x over 2 close parentheses end fraction cross times fraction numerator 1 over denominator cos squared open parentheses straight pi over 4 plus straight x over 2 close parentheses end fraction cross times 1 half
dy over dx equals fraction numerator 1 over denominator sin open parentheses straight pi over 4 plus straight x over 2 close parentheses end fraction cross times fraction numerator 1 over denominator cos open parentheses straight pi over 4 plus straight x over 2 close parentheses end fraction cross times 1 half
dy over dx equals fraction numerator 1 over denominator sin open parentheses straight pi over 2 plus straight x close parentheses end fraction
dy over dx equals 1 over cosx equals secx
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Answered by Sneha shidid | 11th Jul, 2018, 02:34: PM