MathCity.org Merging man and maths

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1 MathCity.org Merging man and maths Exercise 10. (s) Page Textbook of Algebra and Trigonometry for Class XI Available Version:.0 Question # 1 Find the values of sin, and tan when: 1 π (i) (ii) whereo < < 1 1 π (i) ; 0 < < 1 Since ± sin As is in the first quadrant so value of cos is +ive sin and tan 1 1 tan 1 Now sin 1 10 sin cos cos sin tan tan 1 tan ( 1 ) ( 1 ) tan 119 (ii) π ; 0 < < Hint: First find and tan then solve as above

2 FSc I Prove the following identities (Question 1) Question # cot tan cot cos sin L.H.S cot tan (cos sin ) cot R.H.S sin Question # sin tan sin cos L.H.S cos tan R.H.S Question # tan L.H.S 1 cos sin 1 sin sin cos sin 1 sin sin cos tan R.H.S cos Question # sec tan + L.H.S cos sin + + ( sin ) cos + sin cos sin sin 1 sin sec tan R.H.S 1 + cos cos 1 + cos

3 Question 6 sin + cos sin cos L.H.S + sin + cos + sin cos sin cos sin cos sin + cos sin cos sin + cos sin cos R.H.S Question # 7 cosec θ + cosec θ cot θ secθ cosecθ + cosecθ L.H.S secθ 1 + sin θ θ + 1 cos θ θ cot θ R.H.S sin cos Question # tan tan sec sin L.H.S tan tan cos cos + sin cos( ) cos cos 1 sec R.H.S cos FSc I sin + cos 1 sin cos

4 FSc I Question # 9 sin θ tan θ tanθ + cosθ cosθ cos θ sin θ L.H.S cos θ + cosθ cos θ sin θ cos θ 1 cos θ + cos θ sin θ sin θ cos θ cos θ (cos θ 1) sin θ cos θ tan θ tan θ tan θ tan θ R.H.S Question # 10 sin θ cosθ sinθ cosθ sin θ cosθ L.H.S sin( θ θ ) sin θ R.H.S Question # 11 cosθ sin θ + cosθ sinθ cosθ + sin θ L.H.S + sin( θ + θ ) sin θ sin θ ( cos θ )cos θ cos θ R.H.S Question # 1 θ θ tan + cot secθ θ θ cot tan θ θ θ θ sin cos sin + cos + θ θ θ θ θ θ tan + cot cos sin sin cos L.H.S θ θ θ θ θ θ cot tan cos sin cos sin θ θ θ θ sin cos sin cos

5 [[ FSc I θ θ sin + cos 1 secθ R.H.S θ θ cos sin Question # 1 sin θ cosθ + cot θ sinθ cosθ sin θ + cosθ L.H.S + cos( θ θ ) cot θ R.H.S sin θ Question # 1 Reduce sin θ to an expression involving only functions of multiples of θ raised to the first power. sin θ ( sin θ ) cos θ + cos θ 1 ( 1 cos θ + cos θ ) 1 cos θ 1 cos θ + cos θ cos θ + 1 ( cos θ + cos θ ) Question # 1 Find the values of and, without using table or calculator, when θ (i)1 (ii)6 (iii) (iv)7 (i) Let θ 1 θ 90 θ + θ 90 θ 90 θ sin θ sin(90 θ ) sin θ cosθ cosθ cos θ cos θ sin θ cos θ ing by (1 sin θ ) sin θ sin θ sin θ This is quadratic in with a, b 1 and c 1

6 FSc I ± () () ()( 1) ± + ± 0 ± 1± Since θ 1 lies in the first quadrant so value of sin can not be negative therefore Now cos 1 sin 1 cos 1 1 ( ) 1 sin1 θ 1 1 cos cos cos1 (ii) Now cos θ Since cos θ cos θ cos θ 1 cos (1) cos (1) cos sin 6 cos 6 + ( ) cos6

7 FSc I sin6 10 sin6 (iii) Now sin(90 6) cos6 sin cos6 1 + sin And cos(90 6) sin 6 sin(90 θ ) cos sin 6 10 cos (iv) Now sin(90 1) cos1 sin(90 θ ) sin 7 cos sin 7 and cos(90 1) sin1 cos 7 sin1 cos7 1 Alternative Method for Q # 1 (iii) Let θ θ 70 θ + θ 70 sin θ sin(70 θ ) sin θ sin((90) θ ) sin θ cosθ θ θ θ θ sin cos (cos cos ) θ θ θ + θ sin cos cos cos ) θ θ θ 70 θ sin cos + ing by θ θ + sin (1 sin ) θ + θ + sin sin θ θ sin sin 1 sin θ 1 0 This is quadratic in with a, b 1 and c 1 ± () ( ) ( ) ()( 1) ± + cosθ cos θ sin θ ± 0 ± 1± Since θ lies in the first quadrant so value of sin can not be negative therefore

8 FSc I sin θ Now cos sin cos 1 ( ) 1 + cos cos 10 cos Please report us error at Book: Exercise 10. (Page ) Text Book of Algebra and Trigonometry Class XI Punjab Textbook Board, Lahore. Available online at in PDF Format (Picture format to view online). Page setup: A (.7 in 11.0 in). Updated: August,,017. These resources are shared under the licence Attribution- NonCommercial-NoDerivatives.0 International Under this licence if you remix, transform, or build upon the material, you may not distribute the modified material.