**(i) If 5 cosθ – 12 sinθ = 0, find the value of (sin θ + cos θ)/(2 cosθ – sinθ).**

**(ii) If cosecθ = 13/12, find the value of (2 sinθ – 3 cosθ)/(4 sinθ – 9 cosθ).**

**Answer :**

**(i) **5 cosθ – 12 sinθ = 0

5 cosθ = 12 sinθ

⇒ sin θ/cos θ = 5/12

⇒ tan θ = 5/12

Dividing both numerator and denominator by cos θ

**(ii) **cosec θ = 13/12

cosec θ = 1/sin θ

1/sin θ = 13/12

⇒ sin θ = 12/13

Here cos^{2} θ = 1 – sin^{2} θ

= 1 – (12/13)^{2}

= 1 – 144/169

Taking LCM

= (169 – 144)/ 169

= 25/169

= (5/13)^{2}

cos θ = 5/13

Here,

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