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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:

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

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:

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

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

rightwards double arrow space space space sinθ over cosθ plus 1 over cosθ space equals space square root of 3

rightwards double arrow

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Dividing throughout by

square root of left parenthesis square root of 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space 2 comma

we get

fraction numerator square root of 3 over denominator 2 end fraction space cosθ space minus space 1 half sinθ space space space space equals space space space 1 half

rightwards double arrow

cosθ space cos straight pi over 6 minus sinθ space sin straight pi over 6 space equals space 1 half

rightwards double arrow

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rightwards double arrow

straight theta space plus space straight pi over 6 space equals space 2 nπ space plus-or-minus space straight pi over 3 comma space space straight n space element of space straight Z

rightwards double arrow

space space straight theta space equals space 2 nπ plus-or-minus straight pi over 3 minus straight pi over 6 comma space straight n space element of space straight Z

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:

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

104 Views