Trigonometry Past Paper PDF

Exercise 8.3 to change the following to sum or difference. OSe the product-to-sum formula (ii) 2cos 5tsin 3...

Exercise 8.3 to change the following to sum or difference. OSe the product-to-sum formula (ii) 2cos 5tsin 3tx () 4sin 16xcos10x (i) 10cos10y cos6y -2sin(-100°) (iv) 6cos5xsin 10x (v) sin(-)sin5u (vi) )sn(-20') (ix) 2sin 75° sin 15° (vii) cos23° sin 17° (vii) 2cos56°sin 48° 2u-2v (x) 4sin -cos 2cosu 2 2v +2y t -Sin 2 (xi) 2 2. Rewrite the sum or difference as a product oftwo functions. () sin 70° +sin 30° (i1) sin 76° - sin 14° (iii) cos58° +cos12° (iv) cos P9+ 2 cos PT9 2 (v) sin(-10°) +sin(-20°) 3. Prove the following identities. cos(a +B) 1-tan a tan B 6cos&usin2u -3sinlOu () (ii) +3 cos(a- B) 1+ tana tan ß sin(-6u) Sin6u (ii) 4cos4v sin 3v=2/sin 7v-sin v) (iv) sin 30 +sin =4cos sin (v) cos3x+ cosx =2cosxcos2x) (vi) 2tany cos3y =secy(sin4y -sin2y) (vi) sin 6ß+sin4ß co30 +coie =tan 5ß cotß (viil) -cos20 cot8 sin 6ß-sin 48 cot30 -cot® 224 Unit-08 Fundamentals otTrigonometry National Book Foundaia  cos6r+ cos8x cos2a- cos4a (ix) sin 6x-sin 4x =cotxcos 7xsec5x (x) sin 2a +sin 4a = atan ix) 2cos2u cosu+sin2usinu =2cos'u (xii) 2sin2ysin 3y =cosy-cos5y cos10x +cos6x =cot2xcot8x (xiii) cos6x- cos10x Prove that. cos 20° = sin 70°sin 50° sin 30°sin 10° cos80°cos60° cos 40 (i) 16 16 n. 2n.3 47 3 (111) Sinsinsin 9 9 9 sin 9 16 TbaIO LAgrnt