Question

9cosA+12sinA=15.then find the value of cotA?plz answer with a photo

Answer 1

the solution is here ...hope this helps @sumo

Answer 2

Answer:

The value of cotA is 3/4

Step-by-step explanation:

Step 1: Given data 9cosA+12sinA=15

Step 2: Divide 3 on both the sides

3cos A + 12 sin A=5

Step 3: Divide SinA on both the sides

3 cosA/sinA + 4 sinA/sinA = 5/sinA

3cotA + 4 = 5 cosec A  (Therefore cosA/sinA=cotA)

Step 4: To calculate the value of cotA:

Step 5: Squaring on both the sides

Step 6: $(3 \cot A+4)^{2}=(5 \csc A)^{2}$

Step 7: $9 \cot ^{2} A+24 \cot A+16=25 \csc ^{2} A$

$\begin{array}{l}{9 \cot ^{2} A+24 \cot A+16=25(1+\cot 2 A)} \\ {9 \cot ^{2} A+24 \cot A+16=25+25 \cot ^{2} A} \\ {16 \cot ^{2} A+24 \cot A-9=0}\end{array}$

Step 8:(4 cot A – 3)2 = 0

Step 9: 4 cotA-3=0

4cotA-3=0

4cotA=3

The final value of cotA  =  ¾