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CBSE Class 10 Answered

 Prove the following trigonometric identity Cos^2(90°-theta) +Cos^2theta=sec^2(90°-theta) -cot^2theta 
Asked by abulhussain3438 | 28 May, 2020, 08:03: AM
answered-by-expert Expert Answer
To prove: cos2(90°-theta) + cos2theta = sec2(90°-theta) - cot2theta
 co n s i d e r comma
L H S equals cos squared open parentheses 90 minus theta close parentheses plus cos squared theta
equals open square brackets cos open parentheses 90 minus theta close parentheses close square brackets squared plus cos squared theta
equals open square brackets sin theta close square brackets squared plus cos squared theta
equals sin squared theta plus cos squared theta
equals 1
R H S equals s e c squared open parentheses 90 minus theta close parentheses minus co t squared theta
equals open square brackets s e c open parentheses 90 minus theta close parentheses close square brackets squared minus c o t squared theta
equals cos e c squared theta minus c o t squared theta
equals 1
H e n c e comma space cos squared open parentheses 90 minus theta close parentheses plus cos squared theta equals cos e c squared theta minus c o t squared theta
Answered by Renu Varma | 28 May, 2020, 09:40: AM

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