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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°

107 Views

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

136 Views

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

Let us consider two right angle triangles right angled at C and R respectively.

sinB space equals space AC over AB

Now,

Let us consider two right angle triangles right angled at C and R res

and

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But

sin space straight B space equals space sin space straight Q space left parenthesis given right parenthesis

∴

AC over AB equals PR over PQ

rightwards double arrow space space space space space space space space AC over PR equals AB over PQ

Let

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...(i)
In ΔABC,
Using Pythagoras theorem, we have

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increment PQR comma

Using Pythagoras theorem, we have

QR space equals space square root of PQ squared minus PR squared end root

So,

BC over QR equals fraction numerator straight K square root of PQ squared minus PR squared end root over denominator square root of PQ squared minus PR squared end root end fraction equals straight K space space space... left parenthesis ii right parenthesis

Comparing (i) and (ii), we get

AC over PR equals AB over PQ equals BC over QR

So, by using SSS similar condition
∴

space space increment ACB space tilde space increment PRQ

angle straight B space equals space angle straight 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.

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