Question

if 7 sin^2+ 3 cos^2 is equal to 4 show that tan=1/√3​

Answer 1

Answer:

7sin^2+3cos^2=4

to prove:tan=1/√3

solution:4sin^2+3sin^2+3cos^2=4

4sin^2+3(sin^2+cos^2)=4

4sin^2+3(1)=4. [sin^2+cos^2=1]

4sin^2+3=4

4sin^2=4-3

4sin^2=1

sin^2=1/4

sin=√1/√4

sin=1/2

now, sin^2+cos^2=1

so,cos^2=1-sin^2

cos^2=1-1/4

cos^2=4-1/4

cos^2=3/4

cos=√3/√4

cos=√3/2

now, tan=sin/cos

tan=1/2÷√3/2

tan=1/√3

hence proved.....................