udiyASsIgnmentRe 285 points LarAT9 74055 wWrite the tigonome

udiyASsIgnment-Re -/2.85 points LarAT9 7.4.055 wWrite the tigonometric expresion as an algebraic expression Write the trigonometric expression as an algebraic expression. cos(arccos x + arcsin x) Need Help? dTakto a Titer Need Help?Read l Read It Talk to a Tutor

Solution

1) cos ( arc cosx + arc sinx)

cos ( A+B) = CosA cosB - sinA*sinB ---------------------------------1

here A = arc cosx

cosA = x , sinA = (1-cos²A)^1/2 = ( 1-x²)^1/2

B = arc sinx

sinB = x, cosB = ( 1-sin²B)^1/2 = ( 1-x²)^1/2

putting these values in eq 1:

cos(A+B) = x*( 1-x²)^1/2 - ( 1-x²)^1/2*x

= 0

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2) sin ( pi/6 +x) = (1/2)*( cosx + 3^1/2*sinx)

LHS ( use ( sin(A+B) = sinA*cosB + cosA*sinB)

sin( pi/6+x)= sin(pi/6)*cosx + cos(pi/6)*sinx

= (1/2)*cosx + ( 3^1/2 /2)*sinx

= (1/2)*( cosx + 3^1/2*sinx)

= RHS