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Mathematics : Introduction to Trigonometry

Short Answer Type

41. Choose the correct option and Justify your choice.

left parenthesis 1 plus tanθ plus secθ right parenthesis space left parenthesis 1 plus cotθ minus cosecθ right parenthesis

=
(A) 0 (B) 1 (C) 2 (D) -1

128 Views

42. Choose the correct option and Justify your choice.
(sec A + tan A) (1 - sin A) =
(A) sec A (B) sin A (C) cosec A (D) cos A

104 Views

43. Choose the correct option and Justify your choice.

space fraction numerator 1 plus tan squared straight A over denominator 1 plus cot squared straight A end fraction equals

(A)

sec squared straight A

(B) -1 (C)

cot squared straight A

(D)

tan squared straight A

89 Views

44. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

space space left parenthesis cosecθ space minus space cotθ right parenthesis squared space equals space fraction numerator 1 minus cosθ over denominator 1 plus cosθ end fraction.

115 Views

45. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction equals space 2 space secA.

99 Views

Long Answer Type

46. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

fraction numerator tanθ over denominator 1 minus cotθ end fraction plus fraction numerator cotθ over denominator 1 minus tanθ end fraction space equals space 1 plus secθ. space cosecθ

147 Views

Short Answer Type

47. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

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121 Views

Long Answer Type

48. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

fraction numerator cos space straight A minus sin space straight A plus 1 over denominator cos space straight A plus sin space straight A minus 1 end fraction equals cosec space straight A plus cot space straight A.

154 Views

49. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

square root of fraction numerator 1 plus sinA over denominator 1 minus sinA end fraction end root space equals space secA plus tanA.

118 Views

Short Answer Type

50. Prove the following identities where the angles involved are acute angles for which the expressions are defined.

fraction numerator sinθ minus 2 sin cubed straight theta over denominator 2 cos cubed straight theta minus cosθ end fraction equals space space tanθ

103 Views