If `(a+b) alpha sqrt(ab)`, then show that `(sqrta+sqrtb) alpha (sqrta-sqrtb)`.

If sin alpha=(5)/(13) , then show that tan alpha + sec alpha=1.5 .

If sqrta : sqrtb = sqrt3 : sqrt2 " and " sqrtb : sqrtc = sqrt3 : sqrt2 , then find the value of (sqrta + sqrtb ) : ( sqrtb + sqrtc) .

If cosec alpha+cot alpha=2+sqrt(5) , show that, cosalpha=2/sqrt(5) .

If cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .

If tan (alpha + beta) = a + b " and " tan ( alpha -beta) = a-b, "then show that, " a tan alpha - b tan beta = a^(2)-b^(2)

If alpha!=beta and atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2) ,then show that (cosalpha)/(cosbeta)=a/b

If cos alpha+ cos beta= a sin alpha+ sin beta=b , then show that "tan" (alpha)/(2)+"tan" (beta)/(2)= (4b)/(a^(2)+b^(2)+2a)

(a) If x gt a, y gt b and x + y = a + b , then find which one of (sqrtx + sqrty) and (sqrta + sqrtb) is greater ? (b) Which one of the two (sqrt21 + sqrt11) and (2sqrt5 + 2 sqrt3) is greater ? (c) Which one is greater root(3)(4) and root(4)(5) ? (d) Find the greatest and least numbers : 2 sqrt2, 3 root(3)(2), 2 root(4)(3), 2 root(6)(7)

If a sin alpha = b sin beta " then show that ", b cot alpha + a cot beta = (a+b) "cot"(alpha+beta)/2

If a alpha b and b alpha c , show that a^3+b^3+c^3 alpha 5 abc .