Question

If 7sin^2theta+3cos^2theta=4, show that tan theta=1/√3

Answer 1

7sin²@ +3cos²@=4
4sin²@+3sin²@+3cos²@=4
4sin²@+3(sin²@+cos²@)= 4
4sin²@+3=4
4sin²@=4-3
sin²@=1/4
sin@=1/2
p= 1 and h=2

we know that:
b²=h²-p²
b²=2²+1²
b=√(4-1)
b=√3
we know that:
tan@=p/b
tan@=1/√3
_____________proved_________________
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Answer 2

7sin^²Ф + 3cos²Ф = 4

7(1 - cos²Ф) + 3cos²Ф = 4

7 - 7cos²Ф + 3cos²Ф = 4

-4cos²Ф = 4 - 7

cos²Ф = 3/4

cosФ = √3/2

cosФ = cos30

Ф = 30

 now, 

tan30 = 1/√3