38 للا ۹:۵۸ مع . Tan3A - 1 - 3tan A all Coxx-*=*-Cast i Coran Cash + v) - Cosh.Cehu Sinh Sinh 2 536638053905596890... Ca

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38 للا ۹:۵۸ مع . Tan3A - 1 - 3tan A all Coxx-*=*-Cast i Coran Cash + v) - Cosh.Cehu Sinh Sinh 2 536638053905596890... Cash Coshin.Coxli Sinh Sinki XVIT ) COSITSINNVEST +1) -- xviii) Sinhue.Sinhv = [Cosh u + v) - Coshi 1 -»)] (– » xix ) Cosh3=Coshua + 4Sinh u.Coshu = 4Coshu - 3Cosh xx) (Coshx + Sinhx )" - Coshnx + Sinhnx ( 10. If u and deduce formula for Sina, Cose, tant in terms of u. (ans.:(u'-1)(u +7); 2u//u'+1);(u-IV{u+1)) 1 + Sina I 1-Sin Coso prove that 4 Cose 2-tana 11. If Sin( x +a)= 2Cosi r-nl.nove that : tanr = = 1 - 2 tan a 12. If Siner-a) Cos(x + a); prove that : tanrl. 13. If x=Cos+Cos 20 and y Sin 0+ Sin 20 . Show tha': **V ALUSJUTLUSU ii) 2xy = Sin20 +2 Sin 30 + Sin 40 14. If Cos 2A.Cox 2B -Cos 20. prove that: Sin' A.Cox B + Cox A. Sin'B - Sin'e + 15. If S = Sin 0 and C - Cos 0, simplify: S.C S.V1-S с S i) iii -S ) C.V1-C S C (ans.si) Sine; ii); iii) Sec0.Csce) 16. Eliminate from the following equations : i) = a.Cse and y = 5 Seco ) x y= ü) x = Sine+Cose and y=Sine-Cos@ iii) x = Sin+tan and y = Sin 8-lan iv) x = tano and y = fan 20 4 4 4 2x (ans: i), +, -1; il kr +y =2; ii =/; i)y= ry (x+y)(x-y} 2 1-r 17. In the acute-angled triangle OPQ, the altitude OR makes angles A and B with OP and OQ. Show by means of areas that if OP=4, 0Q=p OR=r: p.q.Sin(A+B) = q.r.Sina + p.r. SinB. 18. Given that a = Sin 2 find Cosa , tana, Seca, and Csca. V31 2 (ans.: . 23 13 19. Evaluate the following expressions : TT a) Sin Cos- 2 c) Cot(Cos') c e) Cosí Sin0.8) b) Csc Sec-2) d) Sin-'1-Sin-'(-1) 1) Cor- (-Sin " (ans.: 1/ 12:2/3:0;0,0.6,2x/3) 20. Find the angle a in the below graph (Hint: a+f=65"): 1 65° r: ans.: 42.2) 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions