Mathematics
Assertion (A): 5 cos 40°.cosec 50° = 5.
Reason (R):
5 cos 40°.cosec 50° = 5 cos 40° x cosec (90° - 40°)
= 5 cos 40° x = 5
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Trigonometric Identities
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Answer
Both A and R are true.
Explanation
Given, 5 cos 40°.cosec 50° = 5
Taking L.H.S.
= 5.cos 40°.cosec 50°
= 5. cos 40°.cosec (90° - 40°)
= 5. cos 40°.sec 40°
= 5. cos 40°.
= 5. cos 40°.
= 5.
= 5
Taking R.H.S. = 5
L.H.S. = R.H.S.
∴ Assertion (A) is true.
From the above calculation,
5 cos 40°.cosec 50°
= 5 cos 40° x cosec (90° - 40°)
= 5 cos 40° x
= 5
∴ Reason (R) is true.
Hence, both Assertion (A) and Reason (R) are true.
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