Question

if 12 sin Φ-5 cos Φ =0 then find the value of cot Φ , cosec Φ , and sec Φ​

Answer 1

Answer:

cot Φ=12/5, cosec Φ=13/5 , and sec Φ=13/12

Answer 2

Answer:

CotΦ = B/P = 12/5

CosecΦ = H/P = 13/5

SecΦ = H/B = 13/12

Step-by-step explanation:

12sinΦ-5cosΦ=0

12sinΦ=5cosΦ

Squaring Both Sides

144$sin^{2}$Φ = 25$cos^{2}$Φ

144$sin^{2}$Φ = 25(1-$sin^{2}$Φ)

144$sin^{2}$Φ=25-25$sin^{2}$Φ

169$sin^{2}$Φ=25

$sin^{2}$Φ=25/169

sinΦ=5/13

.: In a Triangle,

Perpendicular(P) = 5

Hypotenuse(H) = 13

Base(B) = $\sqrt{H^{2} - P^{2} }$ = 12

CotΦ = B/P = 12/5

CosecΦ = H/P = 13/5

SecΦ = H/B = 13/12

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