Question

2secA+3tanA=7 and 2tanA+3secA=?

Answer 1

Please see the attachment

Answer 2

It is given that

2 secA+3 tanA=7

Squaring both sides, we get

4 sec²A + 9 tan²A +12 Sec A×Tan A=49

Using the identity

sec²A - tan²A=1

→4 (1 + tan²A) + 9 (sec²A -1) +12 Sec A×Tan A =49

→4 + 4 tan²A + 9 sec²A -9 +12 Sec A×Tan A =49

→4 tan²A + 9 sec²A+12 Sec A×Tan A+4-9=49

→4 tan²A + 9 sec²A+12 Sec A×Tan A=49+5

→(2 tanA+3 secA)²=54

→2 tanA+3 secA =√54=3√6