Question

if 7 sin²θ + 3 cos²θ = 4 then find value of tanθ​

Answer 1

Step-by-step explanation:

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Answer 2

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Answer:

7sin²Ɵ+3cos²Ɵ=4

Step-by-step explanation:

∵sin²Ɵ+cos²Ɵ=1

7sin²Ɵ+3(1-sin²Ɵ)=4

7sin²Ɵ+3-3sin²Ɵ=4

4sin²Ɵ=1

sin²Ɵ=1/4

sinƟ=±1/2

sinƟ=1/2 or (-1/2)

substituting sinƟ in given eq.n;

4-7(1)=3cos²Ɵ

2

4-7=3cos²Ɵ

2

8-7 =3cos²Ɵ

2

1 =cos²Ɵ

6

cosƟ=±1/√6; when sinƟ=(-1/2)

4-7(-1)=3cos²Ɵ

2

4+7=3cos²Ɵ

2

8

8+7=3cos²Ɵ

2

cos²Ɵ=15 = 5

6 2

cos²Ɵ=±5/2; when sinƟ=(1/2)

∵tanƟ=sinƟ/cosƟ

Thus, tanƟ=1 ÷ 5 = 1 (if cosƟ=+5/2)

2 2 5

OR tanƟ=(-1/5) { if cosƟ=-5/2}

tanƟ= (-1/2)÷(1/√6)=(-√6/2)

tanƟ= (-1/2)÷(-1/√6)=(+√6/2)