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Steps to solve Find the general solution for 3sinx+4cosx=5 Put 3=rcosθ and 4=rsinθ ⇒3^2+4^2=r^2.cos^2θ+r^2.sin^2θ ⇒25=r…

Steps to solve Find the general solution for 3tanx+cotx=5cosecx ⇒3tanx+cotx=5cosecx ⇒3(sinx/cosx)+(cosx/sinx)=5/sinx ⇒3…

Steps to solve Find the general solution for 4sin^2x+6cos^2x=5 ⇒4sin^2x+6cos^2x=5 ⇒4sin^2x+6(1-sin^2x)=5 ⇒4sin^2x+6-6si…

Steps to solve Find the general solution for tan^2x+sec^2x=3 ⇒tan^2x+sec^2x=3 ⇒tan^2x+(1+tan^2x)=3 ⇒2tan^2x+1=3 ⇒2tan^2…

Steps to solve Find the general solution for secθ-1=(√2-1)tanθ ⇒secθ-1=(√2-1)tanθ ⇒(1/cosθ)-1=(√2-1)sinθ/cosθ ⇒(1-cosθ)…

Steps to solve Find the general solution for 3tan^2θ-2sinθ=0 ⇒3tan^2θ-2sinθ=0 ⇒3(sin^2θ/cos^2θ)-2sinθ=0 ⇒3sin^2θ-cos^2θ…

Steps to solve find the general solution for cot^2θ-tan^2θ=4cot2θ ⇒cot^2θ-tan^2θ=4cot2θ ⇒(1-tan^2θ)/tan^2θ=4/tan2θ ⇒(1-…

Steps to solve find the general solution for cos2θ=(√2+1)(cosθ-1/√2) ⇒cos2θ=(√2+1)(cosθ-1/√2) ⇒2cos^2θ-1=(√2+1)cosθ-(√2…

Steps to solve Find the value of 2.sin67(1/2).cos22(1/2) =2.sin67(1/2).cos22(1/2) =2.sin(135/2).cos(45/2) =sin{(135/2)+…

Steps to solve Find the value of sin105.cos105 =sin105.coos105 =2.(sin105.cos105)/2 =sin(2.105)/2 =sin210/2 =(1/2)sin(1…

Steps to solve Find the value of sin35+cos5 =sin35+cos5 =sin(90-55)+cos5 =cos55+cos5 =2cos(55+5)/2.cos(55-5)/2 =2.cos60…

Steps to solve Find the value of sin^2(24)-sin^2(6) =sin^2(24)-sin^2(6) =sin(24+6).sin(24-6) =sin30.sin18 =(1/2).(√5-1)…

Steps to solve Find the general solution for sin5θ=sin3θ ⇒sin5θ=sin3θ ⇒5θ=nπ+(-1)^n.3θ ⇒5θ-(-1)^n.3θ=nπ ⇒θ{5-(-1)^n.3}=…

Steps to solve Find the general solution for sin(x+40)=1/√2 ⇒sin(x+40)=1/√2 ⇒sin(x+40)=sinπ/4 ⇒x=nπ+(-1)^n(π/4)-40 ⇒πx/…

Steps to solve  Find the general solutuion for tan^2(3θ)=3 ⇒tan^2(3θ)=3 ⇒tan3θ=√3 ⇒tan3θ=tanπ/6 ⇒3θ=nπ+π/6 ⇒3θ=(6nπ+π)/…

Steps to solve  Find the general solution for tanax=cotbx ⇒tanax=cotbx ⇒tanax=tan(π/2-bx) ⇒ax=nπ+π/2-bx ⇒ax+bx=nπ+π/2 ⇒…

Steps to solve Find the value of (cos15+sin15)/(cos15-sin15) =(cos15+sin15)/(cos15-sin15) =[{(√3+1)/2√2}+{(√3-1)/2√2}]/…

Steps to solve If (1+sinA)/cosA=√2+1, then find the value of (1-sinA)/cosA ⇒(1+sinA)/cosA=√2+1 ⇒{(1+sinA)/cosA}{(1-sin…

Steps to solve  If tanα=1/2 and tanβ=1/3 then fin the value of α+β tan(α+β) =(tanα+tanβ)/(1-tanα.tanβ) =(1/2)+(1/3)/{1-…

Steps to solve   If α and β lie in first and second quadrants respectively and if sinα=1/2, sinβ=1/3 then find the valu…