Question

can any body give me the answer of exercise 8.4 ka question no. 5-(iii)... ; plzzzzzzzzzzz its urgent cbse ncert math book...
trigonometry chapter....

Answer 1

QUESTION:- TAN THETA / 1-COT THETA + COT THETA/ 1-TAN THETA = 1+ SEC THETA COSEC THETA.

ANSWER:- LHS = TAN @ / 1-COT @ + COT @/ 1-TAN @ .

= SIN@/COS@/ 1- COS@/ SIN@ + COS@/SIN@/1-SIN@/COS@

= SIN@ / COS@ / SIN@- COS@/SIN@ + COS@ / SIN@ / COS@- SIN@/ COS@.

= SIN²@ / COS@ ( SIN@-COS@) + COS²/ SIN@(SIN@- COS@).

= 1/SIN@-COS@) × SIN²@/COS²@- COS²@/SIN²@.

= 1/SIN@- COS@ × SIN³@- COS³@/SIN@COS@.

= 1/SIN@-COS@ × SIN@-COS@(SIN²@+COS²@+SIN@COS@)/SIN@COS@.

= 1+SIN@COS@/ SIN@COS@ = 1+ SEC@COSEC@. = RHS....

HENCE,

LHS = RHS..... PROVED....