Find the value of the following-cos 0-sin 45-sin 30-sin90-cos 45- -cos 60-

(cos 0^∘+sin 45^∘+sin 30^∘)(sin90^∘ cos 45^∘ +cos 60^∘) [ 1+1√(2)+12 ] nbsp; [ 1 1√(2)+12 ]= [ 32 +1√(2) ] [ 32 1√(2) ] = ( 32 )^2 ( 1√(2) )^2=94 12=74 ...

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Byju's Answer

Standard IX

Mathematics

Trigonometric Ratios of Complementary Angles

Find the valu...

Question

Find the value of the following:
$(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ})$

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Solution

$(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ}) [1 + \frac{1}{\sqrt{2}} + \frac{1}{2}] [1 - \frac{1}{\sqrt{2}} + \frac{1}{2}] = [\frac{3}{2} + \frac{1}{\sqrt{2}}] [\frac{3}{2} - \frac{1}{\sqrt{2}}] = {(\frac{3}{2})}^{2} - {(\frac{1}{\sqrt{2}})}^{2} = \frac{9}{4} - \frac{1}{2} = \frac{7}{4}$

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Similar questions

Q. Find the value of the following:

(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ})

Q. The value of

(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ})

(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ}) =

Q. Evaluate the following :

(c o s 0^{\circ} + s i n 45^{\circ} + s i n 30^{\circ}) (s i n 90^{\circ} - c o s 45^{\circ} + c o s 60^{\circ})

Evaluate each of the following

$(c o s 0^{o} + s i n 45^{o} + s i n 30^{o}) (s i n 90^{o} - c o s 45^{o} + c o s 60^{o})$

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Find the value of the following: (cos0∘+sin45∘+sin30∘)(sin90∘−cos45∘+cos60∘)

(cos0∘+sin45∘+sin30∘)(sin90∘−cos45∘+cos60∘)[1+1√2+12][1−1√2+12]=[32+1√2][32−1√2]=(32)2−(1√2)2=94−12=74

Find the value of the following:
$(cos 0^{\circ} + sin 45^{\circ} + sin 30^{\circ}) (sin 90^{\circ} - cos 45^{\circ} + cos 60^{\circ})$