Question
What is the simplified value of the given
expression? 3(sinĀ² 30Ā° + sinĀ² 60Ā°) + 6sin 45Ā° - (3sec 60Ā° + cot 45Ā°)Solution
3(sin Ā² 30Ā° + sin Ā² 60Ā°) + 6sin 45Ā° - (3sec 60Ā° + cot 45Ā°)
Using, sin(90Ā° - A) = cos A
= 3{sin Ā² 30Ā° + sin Ā² (90 - 30)Ā°} + 6 x ā2/2 - {3 x 2 + 1}
= 3(sin Ā² 30Ā° + cos Ā² 30Ā°) + 3 - 7
Using, sin Ā² A + cos Ā² A = 1
= 3 x 1 + 3 - 7 = 3 + 3 - 7 = -1
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