AC is the diagonal line joining ABCD(i) tan∠ACD = cot∠ACB⇒ ∠ACD + ∠ACB = 90⇒ tan∠ACD= tan(90 - ∠ACB)= cot∠ACB(ii) tan2∠CAD + 1 = ⇒ tan2∠CAD + 1= cosec2∠ADC[∠ADC = ∠BAC, from the properties]= cosec2∠BAC=

Q. 113.5( 4 Votes )

ABCD is a rectang

Class 10th West Bengal Board - Mathematics 24. Trigonometric Ratios of Complementary Angle

Answer :

AC is the diagonal line joining ABCD

(i) tan∠ACD = cot∠ACB

⇒ ∠ACD + ∠ACB = 90

⇒ tan∠ACD

= tan(90 - ∠ACB)

= cot∠ACB

(ii) tan²∠CAD + 1 =

⇒ tan²∠CAD + 1

= cosec²∠ADC

[∠ADC = ∠BAC, from the properties]

= cosec²∠BAC

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