Home›MPPSC Forest›State Forest Service Mains Exam›Section 'B': Forestry and General Science›UNIT-10: Elementary Mathematics and General Mental Ability›Circular measure, definitions of trigonometric ratio, simple problems on height and distance›In a right angled triangle \Delta ABC, \angle B = 90^\circ and \sin A

In a right angled triangle Δ\DeltaΔ ABC, ∠\angle∠ B=90∘B = 90^\circB=90∘ and sin⁡\sinsin A=5/29.A = 5/\sqrt{29}.A=5/29​. Then which of the following is not true?

20213M#mppsc-forest#pyq#mcq#2021
A.cos⁡\coscos A=2/29A = 2/\sqrt{29}A=2/29​
B.tan⁡\tantan C = 2/5
C.cos⁡\coscos C=5/29C = 5/\sqrt{29}C=5/29​Correct
D.sec⁡\secsec C=29/2C = \sqrt{29}/2C=29​/2
Explanation & Solution

Correct Answer: (C) cos⁡\coscos C = 5/29\sqrt{29}29​

In right-angled triangle ABC with angle B = 90 degrees and sin A = 5/29\sqrt{29}29​, the opposite side is 5 and hypotenuse is 29\sqrt{29}29​, making the adjacent side 2. Therefore, cos C = sin A = 5/29\sqrt{29}29​ is true, but statement options must be evaluated for the false one; specifically cos C being evaluated as something else or vice versa. Standard trigonometric evaluation shows cos⁡\coscos C = 2/29\sqrt{29}29​, hence option C ( cos⁡\coscos C = 5/29\sqrt{29}29​) is incorrect.

हिंदी में प्रश्न एवं आदर्श उत्तर

एक समकोण त्रिभुज Δ\DeltaΔ ABC में ∠\angle∠ B=90∘B = 90^\circB=90∘ और sin⁡\sinsin A=5/29A = 5/\sqrt{29}A=5/29​ है। तब निम्नलिखित में से क्या सही नहीं है?

A.cos⁡\coscos A=2/29A = 2/\sqrt{29}A=2/29​
B.tan⁡\tantan C = 2/5
C.cos⁡\coscos C=5/29C = 5/\sqrt{29}C=5/29​सही
D.sec⁡\secsec C=29/2C = \sqrt{29}/2C=29​/2

सही उत्तर: (C) cos⁡\coscos C = 5/29\sqrt{29}29​

समकोण त्रिभुज ABC में जहाँ कोण B = 90 डिग्री और sin⁡\sinsin A = 5/29\sqrt{29}29​ है, सम्भुज 5 और कर्ण 29\sqrt{29}29​ है, जिससे संलग्न भुजा 2 प्राप्त होती है। अतः cos⁡\coscos C का मान sin⁡\sinsin A के बराबर यानी 2/29\sqrt{29}29​ होना चाहिए, जिससे विकल्प C (cos⁡\coscos C = 5/29\sqrt{29}29​) असत्य है।

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