Question

2sin theta = 3 cos theta . Find sec theta

Answer 1

Answer:

Answer:

3

Explanation:

Given,

sec\theta = \frac{13}{5}secθ=

5

13

---(1)

____________________

We know the Trigonometric identity:

tan² theta = sec² theta -1

= (13/5)² - 1

= 169/25 - 1

= (169 - 25)/25

= 144/25

tan theta = √(12/5)² = 12/5

_______________________

tan\theta = \frac{12}{5}tanθ=

5

12

----(2)

LHS = \frac{2sin\theta -3cos\theta}{4sin\theta - 9cos\theta}

4sinθ−9cosθ

2sinθ−3cosθ

Divide numerator and denominator by cos\thetacosθ ,we get

= \frac{2tan\theta - 3}{4tan\theta - 9}

4tanθ−9

2tanθ−3

= \frac{2 \times \frac{12}{5}-3}{4 \times \frac{12}{5}-9}

4×

5

12

−9

2×

5

12

−3

=\frac{\frac{24-15}{5}}{\frac{48-45}{5}}

5

48−45

5

24−15

= \frac{24-15}{48-45}

48−45

24−15

= \frac{9}{3}

3

9

= 33

= RHS

Step-by-step explanation:

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