61,67 498 CHAPTER 7 Analytic Trigonometrysin (a + B)61.sin a cos B- 1 + cot a tan B60. cos (a + B) + cos (a - B) = 2 cos a cos Bcos (a + B)63.cos a cos B=1- tan a tan Bsin (a + B)62.cos a cos B- tan a + tan Btan a + tan Bcos (a - B)64.sin a cos Bsin (a + B)65.sin (a - Btan a - tan B= cot a + tan Bcot a cot Bcos (a + B)66.cos (a - B)1- tan a tan B%3D67. cot (a + B) =cot B + cot a1 + tan a tan Bcsc a csc Bcot a cot B + 169. sec (a + B) =68. cot (a - B) =cot a cot B-1cot B - cot a71. sin (a - B) sin (a + B) = sin a - sin? esec a sec BВ) -1 + tan a tan B70. sec (a73. sin (0 + km) = (-1)* sin 0, k any integer72. cos (a – B) cos (a + B) = cos? a – sin? ß74. cos (0 + ka) = (-1)k cos 0, k any integerIn Problems 75–86, find the exact value of each expression.76. sin sin-1 V3+ cos275. sin+ cos-77.- cos"!4+ cos-1 5380. cos tan-11278.sin- tan-79. cos tan- sin81. cos82. cos tan- + cos34- tan.83. tan sin- 385. tan sin4+ cos-184. tan86. tan cos1+ sin5cos-niaIn Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictionson u and v.87. cos (cos u + sin¯1 v)88. sin (sinu - cos v)89. sin ( tanu – sin' v)90. cos (tan u + tan-1 v)91. tan (sin- u – cos v)92. sec(tanu + cos"1 v)In Problems 93-–98, solve each equation on the interval 0 se

Question

61,67 498 CHAPTER 7 Analytic Trigonometrysin (a + B)61.sin a cos B- 1 + cot a tan B60. cos (a + B) + cos (a - B) = 2 cos a cos Bcos (a + B)63.cos a cos B=1- tan a tan Bsin (a + B)62.cos a cos B- tan a + tan Btan a + tan Bcos (a - B)64.sin a cos Bsin (a + B)65.sin (a - Btan a - tan B= cot a + tan Bcot a cot Bcos (a + B)66.cos (a - B)1- tan a tan B%3D67. cot (a + B) =cot B + cot a1 + tan a tan Bcsc a csc Bcot a cot B + 169. sec (a + B) =68. cot (a - B) =cot a cot B-1cot B - cot a71. sin (a - B) sin (a + B) = sin a - sin? esec a sec BВ) -1 + tan a tan B70. sec (a73. sin (0 + km) = (-1)* sin 0, k any integer72. cos (a – B) cos (a + B) = cos? a – sin? ß74. cos (0 + ka) = (-1)k cos 0, k any integerIn Problems 75–86, find the exact value of each expression.76. sin sin-1 V3+ cos275. sin+ cos-77.- cos&#34;!4+ cos-1 5380. cos tan-11278.sin- tan-79. cos tan- sin81. cos82. cos tan- + cos34- tan.83. tan sin- 385. tan sin4+ cos-184. tan86. tan cos1+ sin5cos-niaIn Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictionson u and v.87. cos (cos u + sin¯1 v)88. sin (sinu - cos v)89. sin ( tanu – sin' v)90. cos (tan u + tan-1 v)91. tan (sin- u – cos v)92. sec(tanu + cos&#34;1 v)In Problems 93-–98, solve each equation on the interval 0 se < 27.93. sin 0 – V3 cos 0 = 194. V3 sin e + cos 0 = 195. sin 0 + cos e = V296. sin e - cos e = - V297. tan 0 + V3 = sec 098. cot e + csc 0 = - V3Applications and Extensions99. Show that sin (sin v + cos v) = 1.100. Show that cos (sin v + cos v) = 0.A 101. Calculus Show that the difference quotient for f(x) = sin xis given by103. One, Two, Three(a) Show that tan( tan-1 + tan2 + tan&#34; 3) =.(b) Conclude from part (a) thatf(x + h) - f(x)sin (x + h) - sin xtan1 + tan12 + tan¬1 3 = &#34;hhsin h= cos xh1 - cos h- sin xA 102. Calculus Show that the difference quotient for f(x) = cos xis given byhinstantaneous power p at time t is given byp(t) = V„Im cos o sin? (wt) -Vmlm sin o sin(w) af(x + h) – f(x)cos (x + h) - cos xShow that this is equivalent tohsin h= -sin xh1-cos hcos xP(t) = VmIm sin ( wt) sin(»t – 9)h

Accepted Answer

61) we have to prove that:
sinα+βsinαcosβ=1+cotα tanβ