Question

Evaluate each of the following $sin^{2}30^{0}cos^{2}45^{0}+4tan^{2}30^{0}+\frac{1}{2}sin^{2}90^{0} \\-2cos^{2}90^{0}+\frac{1}{24}cos^{2}0^{0}$

Answer 1

SOLUTION :

Given :

sin² 30° cos² 45° + 4 tan² 30° + 1/2sin² 90° − 2 cos² 90° + 1/24 cos² 0°                                      

= (½)² × (1/√2)² + 4(1/√3)² + ½(1)² - 2(0)² + 1/24×(1)²

[sin 30° = ½ ,cos 45° =1/√2, tan 30° = 1/√3,sin 90° = 1,cos 90° = 0, cos 0° = 1]

= ¼ × ½ + 4 × ⅓ + ½ - 0 + 1/24

= ⅛ + 4/3 + 1/ 2 +1/24

= [ (1×6) + (4× 16) + (1×24) + (1× 2)] / 48

[By taking L.C.M of 8,3,2,24. L.C.M is 48]

= (6 + 64 + 24 +2 )/48

= 96/48 = 2

sin² 30° cos² 45° + 4tan² 30° + 1/2sin² 90° − 2 cos² 90° + 1/24 cos² 0° = 2  

Hence, sin² 30° cos² 45° + 4tan² 30° + 1/2sin² 90° − 2 cos² 90° + 1/24 cos² 0° = 2  

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :-

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Evaluate :-

sin² 30° cos² 45° + 4 tan² 30° + 1/2sin² 90° − 2 cos² 90° + 1/24 cos² 0°  

= ( 1 / 2 )² × ( 1 / √2 )² + 4 × ( 1 / √3 )² + 1 / 2 × ( 1 )² - 2 × ( 0 )² + 1 / 24 × ( 1 )²

= 1 / 4 × 1 / 2 + 4 × 1 / 3 + 1 / 2 + 1 / 24

= 1 / 8 + 4 / 3 + 1 / 2 + 1 / 24

= ( 3 + 32 + 12 + 1 ) / 24

= 48 / 24

= 2

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Since ,

sin30° = 1 / 2

cos45° = 1 / √2

tan30° = 1 / √3

sin90° = 1

cos90° = 0

cos0° = 1

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