Explanation:

Let’s break it down step by step:

- Start with the given equation:

3 sec²? + tan? – 7 = 0

Replace sec²? with 1 + tan²?:

- 3(1 + tan²?) + tan? – 7 = 0

? 3 + 3tan²? + tan? – 7 = 0

? 3tan²? + tan? – 4 = 0

- Factor: (3tan? – 4)(tan? + 1) = 0

- ? ? (0°, 90°), so tan? = 4/3 (Since tan? = –1 doesn't fit in this range.)

- Now, use right triangle ratios:

- If tan? = 4/3,

- Opposite/Adjacent = 4/3

- Hypotenuse = v(3²+4²) = 5

- sin? = 4/5,

- cos? = 3/5

- Now answer the question: find

2sin? + 3cos? / (cosec? + sec?)

- 2sin? + 3cos? = 2(4/5) + 3(3/5) = (8+9)/5 = 17/5

- cosec? = 1/sin? = 5/4; sec? = 1/cos? = 5/3

So, cosec? + sec? = 5/4 + 5/3 = (15+20)/12 = 35/12

- The expression is:

(17/5) ÷ (35/12) = (17/5) × (12/35) = (17×12)/(5×35) = 204/175

Let’s check the options:

- Option 1: 10

- Option 2: 5

- Option 3: 5

- Option 4: 4/2

None of these match exactly, from 204/175 ˜ 1.17.

It looks like the options are suspicious or perhaps the question was miswritten or rounding expected.

But if your answer was option 3: 5, let’s compare:

- 2sin? + 3cos? = 17/5

- Denominator is 35/12

- Quotient: (17/5)/(35/12) = 204/175 ? 5

If you want me to clarify any step or re-check with a particular assumption, let me know!