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Trigonometric Functions

Short Answer Type

141.

Find the general solution of:

$sec squared 2 straight x space equals space 1 minus tan 2 straight x$

126 Views

142.
Find the general solution of:

$tan space 2 straight x space equals space tan space straight x$

tan space 2 straight x space equals space tan space straight x space

rightwards double arrow

space space 2 straight x space equals space nπ space plus space straight x comma space space straight n space element of space straight Z

rightwards double arrow

space space straight x space equals space nπ comma space space straight n space element of space straight Z

Hence, the general solution of the equation is

space space space space space space straight x space equals space nπ comma space space straight n space element of space straight Z

Alternative method:

tan space 2 straight x space equals space tan space straight x rightwards double arrow space fraction numerator sin space 2 straight x over denominator cos space 2 straight x end fraction space equals space fraction numerator sin space straight x over denominator cos space straight x end fraction

rightwards double arrow

space space space sin space 2 straight x space cos space straight x space equals space cos space 2 straight x space sinx

rightwards double arrow

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rightwards double arrow

sin left parenthesis 2 straight x minus straight x right parenthesis space equals space 0

[∵ sinA cosB - cosA sinB = sin (A - B)]

rightwards double arrow

sin space straight x space equals space 0

Hence, the general solution of the equation is

space space straight x space equals space nπ comma space space straight n space element of space straight Z

104 Views

143.

Find the general solution of:

$cos space mx space plus space cos space nx space equals space 0$

114 Views

144. Find the general solution of the following trigonometric equation:

square root of 3 space sinx space minus space cos space straight x space equals space square root of 2

110 Views

145. Find the general solution of the following trigonometric equation:

tan space straight theta space plus space sec space straight theta space equals space square root of 3

122 Views

146. Find the general solution of the following trigonometric equation:

tan space straight x space plus space tan space 2 straight x space plus space tan space straight x space tan space 2 straight x space equals space 1

158 Views

147. Find the general solution of the following trigonometric equation:

tan squared straight theta space plus space cot squared straight theta space equals space 2

113 Views

148. Find the general solution of the equation:

cos space 3 straight x space equals space sin space 2 straight x.

96 Views

Long Answer Type

149.

Find the general solution of the equation:

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117 Views

Short Answer Type

150.

Find the general solution of the equations:

$space space space tanx space plus space tan 2 straight x space plus space tan 3 straight x space equals space tanx space space tan 2 straight x space space tan 3 straight x$