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Introduction to Trigonometry

Short Answer Type

111. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 89° + tan 89°

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112. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 69° + cot 69°

110 Views

113. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 75° + cot 75°

98 Views

114. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 70° + cot 70°

94 Views

Long Answer Type

115. In ΔABC, right angled at c,if

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find the value of sinA. cosB + cosA. sinB

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116. If ∠ZB and ∠Q are acute angles such that sin B = sin Q, then prove that ∠B = ∠Q.

125 Views

Short Answer Type

117. In ΔABC right angled at A, given ∠B = 30°, AC = 3 cm. Find AB, BC and ∠ACB.

87 Views

118. Find the value of sin 30° geometrically.

Consider an equilateral ΔABC.
Since each angle in a equilateral A is 60°.
∴ ∠A = ∠B = ∠C = 60°
Draw a perpendicular from A on side BC.
Now, ΔABD= ΔACD => BD = DC
and ΔBAD = ΔCAD [C.P.C.T.]
Consider an equilateral ΔABC.Since each angle in a equilateral A is
Let AB = 2a. Then, $BD space equals space 1 half BC space equals space straight a$
In right ΔADB, by Pythagoras theorem.
$AD squared plus BD squared space equals space AB squared space space rightwards double arrow space space AD squared space equals space AB squared minus BD squared space equals space left parenthesis 2 straight a right parenthesis squared minus straight a squared space equals 3 straight a squared space rightwards double arrow space space space AD squared space equals space 3 straight a squared space rightwards double arrow space space AD space equals space straight a square root of 3$
Now, in right ΔADB,
$sin space 30 degree space equals space BD over AB equals fraction numerator straight a over denominator 2 straight a end fraction equals 1 half.$

1665 Views

119. Find the value of tan 60°, geometrically.

1831 Views

120.

If $sin thin space left parenthesis straight A minus straight B right parenthesis space equals space 1 half comma space space space space space cos space left parenthesis straight A plus straight B right parenthesis space equals space 1 half comma space space space 0 degree less than straight A plus straight B less or equal than 90 degree comma space space straight A greater than straight B.$ Find A and B.

82 Views