Question

find the value of sin² 45°+ cos² 60°+ tan² 30°

Answer 1

• Answer:
• We know that
•        sin45=\frac{1}{\sqrt{2}}sin45=21 , cos30=\frac{\sqrt{3}}{2}cos30=23 , tan 60=\sqrt{3}tan60=3
• Using the above values,
• \begin{gathered
• }sin^245+cos^230-tan^260\
• \\=(\frac{1}{\sqrt2})^{ ^2}+(\frac{\sqrt{3}}{2})^{ {^2}}-(\sqrt{3})^2\\\\=\frac{1}{12+\frac{3}{4}-3\\\\=\frac{2}{4}+\frac{3}{4}-\frac{12}{4}\\\\=\frac{2+3-12}{4}\\\\=\frac{-7}{4}\end{gathered}sin245+cos230−tan260=(21)2+(23)2−(3)2=21+43−3=42+43−412=42+3−12=4−7