ట్రిగోనమెట్రీ – Step-wise Solved Problems (101–120) | High Level

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101. sinθ + cosθ = √2 అయితే θ = ?
Step: max value occurs at 45°
Final Answer = 45°

102. sinθcosθ = 1/2 అయితే θ = ?
Step: max occurs at 45°
Final Answer = 45°

103. (sinθ + cosθ)² = 2 అయితే sinθcosθ = ?
Step: 1 + 2sinθcosθ = 2
sinθcosθ = 1/2
Final Answer = 1/2

104. sin⁴θ + cos⁴θ max value?
Step: = 1 − 2sin²θcos²θ
Max when sin²θcos²θ min (0)
Final Answer = 1

105. sin²θcos²θ max value?
Step: (sinθcosθ)² = (1/2)²
Final Answer = 1/4

106. sinθ − cosθ = 0 అయితే θ = ?
Final Answer = 45°

107. sinθ + cosθ = 0 అయితే θ = ?
Final Answer = 135°

108. tanθ = 1 అయితే sinθcosθ = ?
Step: θ = 45° → sinθcosθ = 1/2
Final Answer = 1/2

109. sinθ = 4/5 అయితే cosθ = ?
Step: √(1 − 16/25) = 3/5
Final Answer = 3/5

110. cosθ = 12/13 అయితే sinθ = ?
Step: √(1 − 144/169) = 5/13
Final Answer = 5/13

111. tanθ = 3 అయితే sinθcosθ = ?
Step: = tanθ / (1 + tan²θ)
= 3/10
Final Answer = 3/10

112. tanθ = 2 అయితే sinθcosθ = ?
Step: = 2 / (1 + 4)
Final Answer = 2/5

113. sin²θ − cos²θ = 0 అయితే θ = ?
Step: sin²θ = cos²θ
θ = 45°
Final Answer = 45°

114. sec²θ − tan²θ = ?
Final Answer = 1

115. cosec²θ − cot²θ = ?
Final Answer = 1

116. sinθcosθ = 1/4 అయితే (sinθ + cosθ)² = ?
Step: = 1 + 2(1/4) = 3/2
Final Answer = 3/2

117. sinθ + cosθ = √3 అయితే sinθcosθ = ?
Step: square → 3 = 1 + 2sinθcosθ
sinθcosθ = 1
Final Answer = 1

118. sin²θcos²θ = 1/16 అయితే sinθcosθ = ?
Final Answer = 1/4

119. sinθcosθ = 1/3 అయితే (sinθ + cosθ)² = ?
Step: = 1 + 2/3 = 5/3
Final Answer = 5/3

120. sinθ + cosθ = 2 అయితే possible?
Step: max value √2 < 2
Final Answer = Not possible

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Shaktimatha Learning | High Level Practice Series