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Find the value of sin50°.

We have to determine the value of sin 50 Solution sin 50 can be expressed as sin50∘=sin(30∘+20∘) From the identity  sin(A+B)=sinAcosB+cosAsinB... View Article

Prove that tan 20 tan 40 tan 80 = tan 60.

Solution: tan20° tan40° tan80°   =2sin20°sin40°sin80°/2cos20°cos40°cos80°   ={cos(20°-40°)-cos(20°+40°)}sin80°/{cos(20°+40°)+cos(20°-40°)}cos80°   =(cos20°-cos60°)sin80°/(cos60°+cos20°)cos80°   ={2cos20°sin80°-2(1/2)sin80°}/{2(1/2)cos80°+2cos20°cos80°} [∵,cos60°=1/2]   ={sin(20°+80°)-sin(20°-80°)-sin80°}/{cos80°+cos(20°+80°)+cos(20°-80°)}   =(sin100°+sin60°-sin80°)/(cos80°+cos100°+cos60°)   ={2cos(100°+80°)/2sin(100°-80°)/2 +√3/2}/{2cos(100°+80°)/2cos(100°-80°)/2+1/2}... View Article

What is the formula of tan3A?

The formula for \(\begin{array}{l}tan (3x) = \frac{(3tanx – tan^{3}x)}{(1 – 3tan^{2}x)}\end{array} \) Derivation We know that \(\begin{array}{l}\tan (A + B)... View Article

If x +1/x=3 then find x^5+1/x^5.

Given X+1/X =3. Therefore (x+1/x)^2=x^2+1/x^2+2 =9, so x^+x^2=7. Similarly,x^3+1/x^3=18 Also,x^5+1/x^5 = (x^2+1/x^2) * (x^3+1/x^3) =x^5+1/x^5+x+1/X= 18×7=126. Hence x^5+1/x^5=126-3=123.