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1 From trig identities ##sin^2x+cos^2x=1## ##therefore 1-sin^2x=cos^2x## ##therefore sec^2x(1-sin^2x)=sec^2x*cos^2x## ##=1/(cos^2x)*cos^2x## ##=1##

##54286.88## gallon Volume of a sphere is given by ##4/3pir^3## where ##pi=3.1416##. Hence spherical water tank will hold ##4/3xx3.1416xx(24/2)^3=4/3xx3.1416xx12xx12xx12## or ##4xx3.1416xx4xx12xx12=7238.25## cubic foot of water or […]

If given the area: The normal area of a circle is ##A=pir^2##. Since a semicircle is just half of a circle the area of a semicircle […]

The polygon will have 40 sides. The measure of the interior angles of a polygon is determined by the formula ##((n – 2)180)/n## = interior angle […]

The height of the sail is ##3m##. The area of a triangle can be calculated as: where ##b## is the length of base and ##h## is […]

##sec2x## ##=1/cos(2x)## ##=1/(cos^2x-sin^2x)## ##=1/(cos^2xsin^2x(1/sin^2x-1/cos^2x))## ##=(1/(cos^2x)1/sin^2x)/(1/sin^2x-1/cos^2x)## ##=(sec^2xcsc^2x)/(csc^2x-sec^2x)##

Use ##cos^2 x + sin^2 x = 1## to find: ##(1-cos^2 x)/(sin x) = sin x## Since ##cos^2 x + sin^2 x = 1## we find: […]

The formula can be proven by applying: 1) Least common multiple; 2) applying the trigonometric entity ##sin^2x + cos^2x=1 ## Head Key-relation : ##sin^2x + cos^2x=1## […]

3 ##cos(x)## has a period of ##2pi## ##cos^2(x)## has a period of ##pi## the only periodic element of this function is the ##cos^2(pi x/3)## which repeats […]