+91-9350504919 support@wiredfaculty.com

Sponsor Area

Principle Of Mathematical Induction

Question

Wired Faculty App

If $WiredFaculty$ show that a, b, c are in A.P.

Solution

space space space tan open parentheses straight A over 2 close parentheses space equals space square root of fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator straight s left parenthesis straight s minus straight a right parenthesis end fraction end root comma space space space tan open parentheses straight B over 2 close parentheses space equals space square root of fraction numerator left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight a right parenthesis over denominator straight s left parenthesis straight s minus straight b right parenthesis end fraction end root comma space space tan open parentheses straight C over 2 close parentheses space equals space square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator straight s left parenthesis straight s minus straight c right parenthesis end fraction end root

tan open parentheses straight A over 2 close parentheses plus tan open parentheses straight C over 2 close parentheses space equals space 2 over 3 cot open parentheses straight B over 2 close parentheses

rightwards double arrow

square root of fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator straight s left parenthesis straight s minus straight a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator straight s left parenthesis straight s minus straight c right parenthesis end fraction end root space equals space 2 over 3 square root of fraction numerator straight s left parenthesis straight s minus straight b right parenthesis over denominator left parenthesis straight s minus straight c right parenthesis left parenthesis straight s minus straight a right parenthesis end fraction end root

rightwards double arrow

square root of fraction numerator straight s minus straight b over denominator straight s end fraction end root open square brackets square root of fraction numerator straight s minus straight c over denominator straight s minus straight a end fraction end root plus square root of fraction numerator straight s minus straight a over denominator straight s minus straight c end fraction end root close square brackets space equals space 2 over 3 square root of fraction numerator straight s left parenthesis straight s minus straight b right parenthesis over denominator left parenthesis straight s minus straight c right parenthesis left parenthesis straight s minus straight a right parenthesis end fraction end root

rightwards double arrow

WiredFaculty

rightwards double arrow

2 straight s minus straight a minus straight c space equals space 2 over 3 straight s

rightwards double arrow

left parenthesis straight a plus straight b plus straight c right parenthesis minus left parenthesis straight a plus straight c right parenthesis space equals space 1 third left parenthesis straight a plus straight b plus straight c right parenthesis

rightwards double arrow

WiredFaculty

rightwards double arrow

2b = a + c

rightwards double arrow

space space straight b equals fraction numerator straight a plus straight c over denominator 2 end fraction

Hence, a, b, c are in A.P.

Some More Questions From Principle of Mathematical Induction Chapter

Find 1 radian angle in degrees, minutes, seconds.

Sponsor Area

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation