Question

If 7 sin² A +3 cos²A= 4, show that tanA=1/V3​

Answer 1

Step-by-step explanation:

Answer is in the pic.

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Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

LHS

7 sin^2 A + 3 cos^2 A = 4

As we know that :-

${\boxed{\sf\:{sin^2 A+cos^2 A=1}}}$

Hence,

7 sin²A + 3 cos²A = 4 × 1

7sin²A + 3 cos²A = 4(sin²A + cos²A)

7sin²A + 3cos²A = 4sin²A + 4cos²A

sin²A × (7 - 4) + 3cos²A = 4cos²A

3sin²A + 3cos²A = 4cos²A

3(sin²A + cos²A) = 4cos²A

3 = 4cos²A

$\tt{\rightarrow\dfrac{1}{cos^2 A}=\dfrac{4}{3}}$

$\tt{\rightarrow sec^2 A=\dfrac{4}{3}}$

$\tt{\rightarrow sec^2 A - 1=\dfrac{4}{3-1}}$

As we know that :-

${\boxed{\sf\:{sec^2 A-1=tan^2 A}}}$

Hence,

$\tt{\rightarrow tan^2 A =\dfrac{4-3}{3}=\dfrac{1}{3}}$

$\tt{\rightarrow tanA=\dfrac{1}{\sqrt{3}}}$