Question

Prove that Cos^2 49 + Cos^2 41/ Sin^2 31 + Sin^2 59 + 2 tan 35 tan 55 =3

Answer 1

Hey your answer is in the given attachment

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Answer 2

$\huge{\orange{\fbox{\green{\fbox{\mathcal{\orange{An}\blue{sw}\green{er}}}}}}}$

$\large{\orange{\fbox{\green{\fbox{\mathcal{\orange{No}\green{te}}}}}}}$

• $\orange{sin(90-\theta)=cos(\theta)}$
• $\blue{cos(90-\theta)=sin(\theta)}$
• $\green{tan(90-\theta)=cot(\theta)}$$\orange{sin^2(\theta)+cos^2(\theta)=1}$
• $\blue{tan(\theta).cot(\theta)=1}$

$\large{\orange{\fbox{\green{\fbox{\mathcal{\orange{Sol}\blue{ut}\green{ion}}}}}}}$

• $\large{\green{Considering\;L.H.S}}$
• $\orange{\dfrac{cos^2(49)+cos^2(90-49)}{sin^2(31)+sin^2(90-31)}+2tan(35)tan(90-35)}$
• $\blue{\dfrac{cos^2(49)+sin^2(49)}{sin^2(31)+cos^2(31)}+2tan(35)cot(35)}$

• $\green{\dfrac{1}{1}+2(1)}$

• $\orange{3}$

• $\blue{Hence,\;\dfrac{cos^2(49)+cos^2(41)}{sin^2(31)+sin^2(59)}+2tan(35)tan(55)=3}$
• $\green{Therefore\;the\;above\;result\;is\;proved}$