Question

If 2sec theta + 3 tan theta=7 then find
3sec theta + 2 tan thata

Answer 1

2sec theta+3tan theta=7
2(1/cos theta)+3(sin theta/ cos theta)=7
(2+3sin theta)/cos theta=7
2+3sin theta=7cos theta
cos theta=(2+3sin theta)/7

3sec theta+2tan theta
=3(1/cos theta)+7(sin theta/cos theta)
=3(7/2+3sin theta)+7(7×sin theta/2+3sin theta)
=(21+49sin theta)/(2+3sin theta)


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Answer 2

2 sec Ф + 3 tanФ=7

Squaring both sides gives

4 sec²Ф + 9 tan²Ф+12 secФtanФ=49

using the identity, Sec²Ф-tan²Ф=1 in the above equation

→4(1+tan²Ф)+9(Sec²Ф -1)+12 secФtanФ-49=0

→4 tan²Ф+9 Sec²Ф+12 secФtanФ-49+4-9=0

→(2 tanФ +3 SecФ)²-54=0

→(2 tanФ +3 SecФ)²=54

→2 tanФ +3 SecФ=√54