Question

if 3cot theta= 4 find the value of 4 cos theta-sin theta /2 cos theta + sin theta​

Answer 1

Answer:

13/5

Step-by-step explanation:

3cot theta= 3 cos theta/sin theta that is equal to 4

so cos theta equals to 4/3 din theta

After putting the value of cos theta in 4 cos theta-sin theta /2 cos theta-sin theta u will get 13/5

Answer 2

Solution

Given that 3cot∅ = 4

$\implies \: \boxed{ \sf{cot \theta = \frac{4}{3} }}$

We have,

$\sf{ \frac{4cos \theta - sin \theta}{2cos \theta + sin \theta}}$

•Dividing both numerator and denominator by sin∅,we get:

$= \sf{ \frac{4cot \theta - 1}{2cot \theta + 1} } \\ \\ = \sf{ \frac{4 \times \frac{4}{3} - 1 }{2 \times \frac{4}{3} + 1 } } \\ \\ = \frac{ \frac{16}{3} - 1 }{ \frac{8}{3} + 1 } \\ \\ = \frac{16 - 3}{8 + 3} \\ \\ = \frac{13}{11}$

Basic Trigonometric Relationships:

• sin∅ = 1/cosec∅

• cos∅ = 1/sec∅

• tan∅ = 1/cot∅ = sin∅/cos∅

• sin²∅ + cos²∅ = 1

• cosec²∅ - cot²∅ = 1

• sec²∅ - tan²∅ = 1