Question:
Exam fear introduction trigonometry part 9 I need to how u got -4 and +4
Answer:
Given, (sin 30 + tan 45 - cosec 60)/(sec 30 + cos 60 + cot 45)
= (1/2 + 1 - 2/√3)/(2/√3 + 1/2 + 1)
= (3/2 - 2/√3)/(3/2 + 2/√3)
= {(3√3 - 2*2)/2√3}/{(3√3 + 2*2)/2√3} { LCM(2, √3) = 2√3 }
= {(3√3 - 4)/2√3}/{(3√3 + 4)/2√3}
= (3√3 - 4)/(3√3 + 4)
Now, we rationalize denominator,
So, we multiply (3√3 - 4) in numerator and denomiantor, we get
= {(3√3 - 4)*(3√3 - 4)}/{(3√3 + 4)*(3√3 - 4)}
= {(3√3 - 4)2 /{(3√3)2 - 42 }
= {(3√3)2 + 42 - 2 * 3√3 * 4}/(27 - 16)
= {27 + 16 - 24√3}/11
= (43 - 24√3)/11
So, (sin 30 + tan 45 - cosec 60)/(sec 30 + cos 60 + cot 45) = (43 - 24√3)/11
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