Question

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Question 1) Find Value of $\rm{cos\:60^\circ\times cos\:30^\circ+sin\:60^\circ\times sin\:30^\circ=}$
Question 2) Find Value of $\rm{sin^2\:45^\circ+cos^2\:45^\circ+tan^2\:45^\circ}$

Answer 1

$\rm{cos\:60^\circ\times cos\:30^\circ+sin\:60^\circ\times sin\:30^\circ=1/2\times\sqrt{3}/2+\sqrt{3}/2\times1/2}$

$\longrightarrow\rm{cos\:60^\circ\times cos\:30^\circ+sin\:60^\circ\times sin\:30^\circ=\sqrt{3}/4+\sqrt{3}/4}$

$\longrightarrow\rm{cos\:60^\circ\times cos\:30^\circ+sin\:60^\circ\times sin\:30^\circ=2(\sqrt{3}/4)}$

$\longrightarrow\rm{cos\:60^\circ\times cos\:30^\circ+sin\:60^\circ\times sin\:30^\circ=\sqrt{3}/2}$

$\rm{sin^2\:45^\circ+cos^2\:45^\circ+tan^2\:45^\circ=(1/\sqrt{2})^2+(1/\sqrt{2})^2+1^2 }$

$\longrightarrow\rm{sin^2\:45^\circ+cos^2\:45^\circ+tan^2\:45^\circ=1/2+1/2+1 }$

$\longrightarrow\rm{sin^2\:45^\circ+cos^2\:45^\circ+tan^2\:45^\circ=2/2+1 }$

$\longrightarrow\rm{sin^2\:45^\circ+cos^2\:45^\circ+tan^2\:45^\circ=1+1=2 }$

Answer 2

Answer:

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