\cos^{2}45^{\circ}+\cos^{2}135^{\circ}+\cos^{2}225^{\circ}+\cos^{2}315^{\circ}=

AP ICET 2015 Paper

Question : 124 of 200

Marks: +1, -0

\cos^{2}45^{∘}+\cos^{2}135^{∘}+\cos^{2}225^{∘}+\cos^{2}315^{∘}=

Solution:

\cos135^{∘}=\cos(180^{∘}-45^{∘})=-\cos45^{∘}

\cos255^{∘}=\cos(180^{∘}+45^{∘})=-\cos45^{∘}

\cos315^{∘}=\cos(360^{∘}-45^{∘})=\cos45^{∘}

∴[\cos^{2}45^{∘}+\cos^{2}135+\cos^{2}225^{∘}+\cos^{2}315^{∘}

=\cos^{2}45^{∘}+(-\cos45^{∘})^{2}+(-\cos45^{∘})^{2}+(\cos45^{∘})^{2}

=4\cos^{2}45^{∘}=4×({1}/{√{2}})^{2}=2

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