[" 7.यदि "sin A=(1)/(sqrt(1+m^(2)))" तो "tan A" बराबर है- "],[[" (i) "1," (ii) "ul(m)]]

Prove that (i) "cos " 15^(@) - " sin " 15^(@) = (1)/(sqrt(2)) (ii) " cot " 105^(@) - " tan " 105^(@) =2sqrt(3) (iii) (tan 69^(@) + tan 66^(@))/(1-tan 69^(@) tan 66^(@)) =-1

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

(sqrt(1+sin 2A)+sqrt(1-sin 2A) )/(sqrt(1 + sin 2A)-sqrt(1-sin2A)) If |tan A| < 1 , and | A I

(sqrt(1+sin 2A)+sqrt(1-sin 2A) )/(sqrt(1 + sin 2A)-sqrt(1-sin2A)) If |tan A| < 1 , and | A I

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) For a=sqrt(2),if a tangent is drawn to a suitable conic (Column 1) at the point of contact (-1,1), then which of the following options is the only CORRECT combination for obtaining its equation? (I) (ii) (Q) (b) (III) (i) (P) (II) (ii) (Q) (d) ("I")("i")("P")

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) If a tangent to a suitable conic (Column 1) is found to be y=x+8 and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination? (III) (ii) (Q) (b) (II) (iv) (R) (I) (ii) (Q) (d) (III) (i) (P)

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) The tangent to a suitable conic (Column 1) at (sqrt(3),1/2) is found to be sqrt(3)x+2y=4, then which of the following options is the only CORRECT combination? (IV) (iii) (S) (b) (II) (iii) (R) (II) (iv) (R) (d) (IV) (iv) (S)

If m=7+4 sqrt(3),(sqrt(m)+(1)/(sqrt(m)))=? / यदि m = 7 + 4 sqrt(3) , ( sqrt( m) + (1)/( sqrtm ) ) = ?