(i) Factorize: sin³θ + cos³θ
Hence, prove the following identity:


(ii) In the given diagram, O is the centre of the circle. PR and PT are two tangents drawn from the external point P and touching the circle at Q and S respectively. MN is a diameter of circle . Given ∠PQM = 42^o and ∠PSM = 25^o

Find :
(a) ∠ OQM
(b) ∠ QNS
(c) ∠ QOS
(d) ∠ QMS

(iii) Use graph sheet for this question. Take 2 cm = 1 unit along the axes.
(a) Plot A(O, 3), B(2, 1) and C(4, -1).
(b) Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
(c) Reflect point A in the line BB' and name its images as A'.
(d) Plot and write coordinates of point A'.
(c) Join the points ABA'B' and give the geometrical name of the closed figure so formed.

Solution

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